Osgiliath

Demographics

The Wall of Charles V included space for 150,000 inhabitants. So if we keep Paris as our model, this gives us a maximum population for the city at its height.

Government

It makes sense given the geography that Osgiliath would have been the ideal location for the capital of Gondor. It also makes sense that when it was, Osgiliath was the largest city. Minas Tirith was a fortified outpost of little significance at this point. When Minas Morgul fell, Osgiliath naturally was much more exposed. Yes, this threaten trade in such a way that prosperity naturally declined. But almost as important is the relocation of the capital. A seemingly resurgent and powerful enemy that now threatens the capital would justify the relocation of the royal family and essential government functions.
The problem is that strips much of the prestige from a city that would drive investment. Real estate is boosted by the elites trying to move closer to the center of power. Those employed in government agencies naturally are concentrated in a capital. These factors can increase the value of military, real estate and luxury good sectors. Plus, the spending of government employees provides a sort of multiplier effect, driving up demand across the city. So moving the city would remove one of the main pillars propping up the local economy.
One thing that was done at the real life London Bridge is sticking heads on pikes. Whenever someone was executed, their heads were boiled and put on display at the southern end of the bridge. At one time there were 30 such heads on display. I have no evidence for what sort of criminal punishments were common in Gondor. But executions and burning at the stake were common in real life medieval Europe. So too were punishments based on public humiliation, like the stocks. The Great Bridge of Osgiliath was the center point of the government district and was highly visible. Plus the eastern end was under more common attack. So this phenomenon would likely be replicated, just on the western side.

Defences

So, Osgiliath was built at a time when Gondor was just founded as a purpose built as the capital. It retained this status and grew to the largest city in Gondor for a long time. So we can assume that it would have pretty decent defenses. Though these would probably have declined over time. Especially on the Eastern side of the river. This was the area most often attacked and occupied by Mordor. Though Boromir was able to retake the whole city in the movies.
This means we can expect the city would have several haphazard defenses and accidental internal divisions. This would be the result of the evolution and expansion of the city. At first, there would be a smaller set of walls protecting the original settled area. But naturally, a capital city will see population growth - especially as the population and territory of Gondor as a whole increases. As a result, future kings would want to add additional layers to incorporate the newly developed areas. Old walls can be expected to over time be consolidated and renovated. Those too out of date, expensive to maintain or inconvenient will be destroyed. This material can then be recycled into the new construction or renovations.
Which means that Paris can be a solid model for us to use. It is a capital city of a medieval great power. It too had walls that evolved like this over time. It also was located on both sides of the Seine, similar to the set up of Osgiliath. Which means it would probably offer a solid basis for inspiration.
The Wall of Philip Augustus was the first of the stone walls of Paris. Again, deep and wide ditches were used. These walls were between six and eight meters high and three meters thick. Construction involved rubble and mortar with a limestone face. The top had a 2 meter wide path with battlements on the outside. The towers were impressive though. There were 77 ones on the main walls placed at 60 meter intervals. Each was 15 meters high, had 6 meter diameters and one meter thick walls. Entrance through these walls were through 15 gatehouses. They had two wood doors reinforced with a portcullis. Each had two 8 meter diameter towers on each side.
But most impressive was the 4 main towers. These were on each side of the river where the walls meet the banks. They were 25 meters high with a 10 meter diameter. Weirdly, the staircase was in an adjacent, connected tower that extended past the top of the main tower. At night, huge chains connected the towers on either side to block unauthorized access by ships. These theoretically could be broken by a ship charging straight at these chains. But this required a huge boat to pull off. It was generally easier to seize the towers controlling them and cut the chain loose.
But the construction of the Phillip II Augustus walls demonstrate a key element that would be carried over to Osgiliath. Namely the strategic priority given to certain sections over others. The Right Bank was finished first. Partially this was due to the fact that the left bank was less developed, so if it fell, there would be less value lost. But more important was the Right Bank was the most accessible part of the city to British controlled territory. Which meant that this was the most likely to be attacked. So we can expect that the first layer of walls of Osgiliath would be on the eastern side facing Mordor. For similar reasons, this would likely be the only portion of the Eastern side of the city in Gondor's hands before Mordor's main assault in the War of the Rings.
Also important to note is that the western bank of Osgiliath was occupied by Gondor until the final assault took place. Which means that the bridge tower on that side would be intact or repairable. So it could become a form of improvised keep.
The local defenses would be manned by the local Urban Cohorts. For a city in decline like this, resources would be limited. Which means a likely force of 1 per 300 people. This translates to only 45 defenders. This is hardly anything. But would probably be the best that can be managed by local officials. Which means the guilds would probably have their own private security forces.

Industry & Trade

So, the River Anduin runs through the center of the city. This would have been the main Gondorian highway system. I would imagine that for no other reason than the value of rivers in medieval societies, the city would have some people living in it. Just significantly fewer than otherwise. There is also a north to south road that runs past the city that serves as the main land route through the same area. Which makes sense given the mountains in the area give few other options. It matters not whether you want to take a boat or wagon - you are going past Osgiliath.
So it would remain the center point for the merchants and ship builders of Gondor. Trade would have been one of the biggest economic drivers. The exports of Gondor would run through here. And most tragically, the export of slaves would pass through here. We can assume that there would be major markets, ship builders, warehouses and slave quarantine areas.
Though trade would have certainly declined significantly. Umbar would certainly disrupt trade coming from the south through corsair raids and simply being a part of a separate political entity. But it would send some, primarily in the form of slaves and plantation products. More important would be the impact of the loss of Minas Morgul. When that city fell, all east-west trade was cut off. Especially that generated from the potentially fertile farmland of Nurn. Then there is the increase in orc attacks that such a base would produce, furthering the trade up and down the river. All this to say that Osgiliath's decline would certainly be a thing, but also would not be near bad enough to turn the city into a ghost town.
The main bridge was the intersection of the Anduin and the road between Minas Tirith and Minas Morgul. It would likely be here in these towers that the tolls would be charged. When it still stood, the impacts of how I see it being constructed leads me to think that any goods going past it would have to be unloaded on one side and packed into another boat on the other. This would slow down trade a lot. But this would not be contested due to the fact that this would make tolls easier to collect and probably benefit related guilds.
Here is where things start to get interesting to me. The destruction of the Bridge would actually make trade from south of Osgiliath to the north. The river would be freer of the rapids and the built obstacles that the bridge formed. By this point, it is likely that the related infrastructure would all be concentrated on the western side of the river. But it would still be there. Basically, all other things being equal, more ships would be passing through the city.

Infrastructure

We don't know much about Osgiliath's infrastructure. But we know that it would be in a state of serious decline. We also know that this decline allows for the sewers to fall out of use. Enough that Faramir is able to lead Frodo and Sam out of the city secretly through them. This could prove valuable for the defense of the city.

History

Osgiliath's story is one of constant decline. Originally, the city was Gondor's capital. The fighting of the Kin-strife naturally found its way here, burning the city. It was hit hard later by the Great Plague. The decision was made to relocate the capital to Minas Tirith. At this point Osgiliath's decline was terminal and the city was totally abandoned.
This did not bode well though for Gondor. Mordor was able to exploit this to seize the city and destroy the main bridge across the river. This attack was the first reported appearance in battle of uruk-hai. But this was not enough, as Gondor did manage to beat the enemy back. Mordor's main invasion during the War of the Ring took the eastern side of the city. Boromir led the defenses well enough to contain the advance and stop them from crossing over. The front stabilized here until the time came for Minas Tirith. The full might of Mordor was thrown into the city and the defenders were overwhelmed.

Architecture

The most notable building in Osgiliath was essentially a bridge complex. The bridge itself was huge and made of stone. At the center was the tower with the Dome of Stars. This hosted the city's Palantír and the Great Hall of the Kings. As one could guess, this was impressively large and topped with a dome.
So, I think this bridge in real life would most likely be a glorified version of the "Old" London Bridge. Just of course modified to be suitably grandiose but practical. Which means to me that I will suggest that each end would be a gatehouse - with two towers flanking them similar to the biggest towers of the walls of Minas Tirith. After all, these would form the start of the defenses for the seat of royal power in the hey day of the city. So one needs these to be as impressive as possible - both to defend the bridge and awe everyone. Which means a pentagonal tower 20 meters tall and 12 wide at each end. Over the river would be a drawbridge.
The London Bridge itself was 8 meters wide and about 270 meters long. It was supported by 60 foot tall stone piers. The path itself was only 4 meters wide and divided into two lanes. The rest of the road was overloaded with at one point a chapel, a public latrine dumping into the river and 138 shops. A total of 200 buildings were on the bridge by 1577. Some of these were 7 stories tall and overhung the road so much that a virtual tunnel was formed.
One of these was a house called the Nonsuch House. Important for our purposes is the fact it straddled the bridge and was 4 stories tall. It could be seen across the city. The building was only 27 feet wide. The Interesting thing for me is that with only 4 stories, it was three shorter than the tallest the London Bridge hosted at some point. Even then, it was a visible point on the skyline.
Which means that the Nonsuch House can be given a significant height upgrade as the Dome of Stars. Especially if made of stone and centered on the strongest piers making the bridge. Should this be rounded off to form a circle, you essentially have a pretty solid tower here. Yet is still practical and serves as the epic center point of the city. Which also allows us to keep the hugely impressive royal center on the bridge while retaining its awe inspiring power.
Sabine, Ernest L., "Latrines and Cesspools of Mediaeval London," Speculum, Vol. 9, No. 3 (Jul. 1934), pp. 305–306, 315. Earliest evidence for the multi-seated public latrine is from a court case of 1306.
Pierce, Patricia, Old London Bridge – The Story of the Longest Inhabited Bridge in Europe, Headline Books, 2001, ISBN 0-7472-3493-0.
The other major building relevant on the London Bridge is the Chapel of St. Thomas on the Bridge, named after a famous troublesome priest. It was built into the pier it was supported by. It was expanded to have three floors, giving it a height of 12 meters. Its footprint was 18 by 6 meters. The first level had an impressive vaulted ceiling 6 meters high. Two doors separated by a 12 meter arched window faced the street. Access could also be granted via a spiral staircase from the second floor and a door leading to a landing at the base of the pier. This latter option allowed boats to dock and send people up into the chapel.
So, why am I talking about a chapel here? Gondor does not have any organized religion as far as I can tell. But, there was the issue of the English Reformation. The chapel was converted into a warehouse, grocer and stationary store at different points. Which means a building of this size and shape can be useful in storing the supplies needed for the government complex that the Great Bridge of Osgilath houses.
But more important to me is the river access down the pier. This facilitates the collection of tolls and inspecting cargoes. Meaning on top of the warehouse role, the "chapel" could effectively be the center of the main customs enforcement of the bridge for river traffic. Supplies could also be carried up to the bridge from here too. The result is that the bridge could be besieged from both sides, yet the Dome of Stars could theoretically hold out forever. Due to this rather important role in the control of the river and resupply of the critical royal center, I suspect that the original headquarters of the Tower Guard would probably be here.
Thomson, Richard (1827), Chronicles of London Bridge, Smith, Elder & Co, London
Now, this over development of the Bridge had some problematic side effects on transit. The buildings forced traffic to move single file in each direction - when meant going across could take a full hour. For this reason the bridge was widened to 14 meters. Then, the large bases of the bridge constrained river traffic in a similar way. It even constricted water flow so much that the area upstream was more prone to flooding. Which then forced more people over the bridge due to ferries were no longer able to move. All of this led to increased fire risk and fatal accidents.
The addition of water wheels did not help. They were added to run grain mills and water pumps. But when their effects were combined with the already constricted water flow from the support piers, boat traffic under the bridge was left only to small boats piloted by the reckless and stupid. Basically, the water level could be as much as 2 meters lower. This created dangerous rapids. Fatal accidents occurred due to people going under the bridge too.
All this to say that the The Great Bridge of Osgiliath could easily be the sort of center for Gondor's political life. There is clearly enough space to concentrate major political offices on it and run high level administration from here. This includes even the palace of the King.

Geography

One thing that is easy to over look is the closeness of all the events surrounding the Return of the King. Osgiliath is literally half way between Minas Tirith and Minas Morgul. You can see Minas Morgul from Minas Tirith. Which means that Osgiliath is an important place in Gondor's geography. It essentially was at the nexus of all the trade and communication links for the whole kingdom.
More important is the fact that the location of Osgiliath was practically the only place armies could cross the river. So gaining control over it would be essential for Mordor if it were to defeat Gondor. Similarly, making Osgiliath as hard to get around would go a long way into protecting Minas Tirith. After all, we know from the main story that the arrival of the Rohirrim and Army of the Dead were both essential for Minas Tirith surviving. But their arrival means nothing if the Minas Tirith falls before their arrival. Delays forced by a determined defense at Osgiliath can contribute greatly towards making sure Minas Tirith ultimately survives.
Wall of Philip Augustus protected 253 hectares of land. Charles V extended the walls on the right bank to include an additional 186 hectares. This extended the city limits to include a total of 439 hectares. The 1791 Wall of the Farmers-General covered 3,402 hectares. The 1844 Thiers Wall covered 7,802 hectares.

Population

13,510

Owning Organization

Gondorian State