Rivendell

Rivendell from a political perspective is one of the luckiest. To its direct north and south are the impassible Misty Mountains. Moria would be friendly as discussed elsewhere. Very close is Lothlorien. Elrond's wife is the daughter of the Lord and Lady of Lothlorien. Plus Galadriel and Elrond both have Elven Rings and are on the white Council. Seems unlikely that Lothlorien would be an issue. Mirkwood is also an elven kingdom that would serve as a buffer state. Mordor, Dol Guldur and the Easterlings all would have to fight their way through Mirkwood to get to Rivendell. Gondor, due to the cultural and political shared history, soft power and political assistance provided I think both Rohan and Gondor would be allies and important buffer states. So, any force that approaches from the east that gets close enough to Rivendell is probably so powerful by that point there is no real hope of victory.
To the west, there is the depopulated area that used to be Arnor. The closest thing this area had to rulers were the same people raised by Elrond in Rivendell. Then there was the Shire. One is weak indeed if the hobbits are seen as much of a threat. Especially when only individual hobbits would be "adventuresome" and only then under the direction of Elrond's ally Gandalf. Beyond that are the elven and dwarven domains on the coast. Both of these are so far away to be a threat and lack the military power needed. So they would not be a threat even if they did decide to fight through Arnor and the Shire just to screw with Elrond.
The result is virtually no one would be a threat to Rivendell. Only Mordor stands out in this regard. Here, the threat calculations would be pretty standard. Mordor has the historical precedents and motive to attack. Plus a large enough army that is likely good enough to be a threat. He would want to wipe out the entire domain due to his spiteful nature - threatening all fixed priorities. Mordor would this be a global, long range, high intensity, expanding, multinational, conventional and lethal military threat.
But as hinted at above, there is virtually no real possibility of Sauron getting to Rivendell. He would have to fight through Gondor, Rohan, Mirkwood and Lothlorien. Moria would probably send troops to help and thus would be a wise target to defeat too. Then there is the Lonely Mountain. The Easterlings would be a wise addition to Mordor's army in this campaign, but would have to defeat Mirkwood, the Iron Hills and the Lonely Mountain first. So, it is most likely that by the time Rivendell is under direct threat from Mordor or the Easterlings, there would basically be no hope left. Probably Sauron would have the One Ring in this scenario, in which case Elrond's Ring would be useless. So the likely result is Rivendell would just evacuate and wage a guerrilla campaign as they retreat to the coast.

Government

Now, due to its location and reputation as a refuge, it was a logical place to host the Council of Elrond. It was also one of the more significant places in terms of historical preservation due to the relics housed and cared for in Rivendell. Then there is the whole sheltering and educating the heirs of Isildur - the most important for our purposes is Aragorn. The result is Rivendell, for all practical purposes, is the center point of elven soft power and coalition building. And thus it is a symbol of how Elves operate and the center of their place in the international order.

Defences

Rivendell appears to be very well defended. It withstood Sauron during a war that the elves otherwise were losing. Later, the Witch King attacked and again lost. These two events solidified Rivendell as a critical position for the Free People and specifically elves.
Due to its location it became semi isolated and somewhat stuck in the past. Yet those who knew now to get to it found it a great place for learning, healing and sanctuary. So, I suspect that Rivendell's defenses would be a bit different than the rest of the elven domains, mainly due to its location. The mountains it is located in does not allow for the forest and earthwork based defenses of the other two main elven kingdoms. Instead, I suspect that Rivendell would prefer stone forts. This would not be an issue - it was founded when Moria was still going strong. Elrond had a very close friendship with Gondor and Moria, two of the best cultures in Middle Earth regarding masonry. So access to the skills and raw amterials would not be an issue even if the elves do not specialize in these themselves.
Now, the terrain around the main settlement suggests that hillside forts would be the most likely form this would take. From the descriptions of the Misty Mountains I have seen, the tops of mountains would be extremely impractical.
Spur castles are a possibility, but I cannot find depictions that suggest that the needed spur is anywhere near Rivendell. These forts though would be the ideal. Essentially, steep cliffs protect three sides from approach. A ditch and a series of wards would then defend the one side that can be attacked. This is one of the most defensible positions out there.
More likely would be a promontory fort, which overlooks a cliff. Or a hillside fort or castle - built on a mountain but not on the top. Both of these are much more accessible and more practical in the inhospitable terrain of the Misty Mountains. These also have a real world tradition of being used to control the trade routes below them. But they also are more easily flanked from the rear and thus harder to defend from that side. Though hillside forts are harder to approach from behind, any enemy that can pull it off would have the height advantage that the castle was meant to provide to the defenders. Normally this would not be a problem though. But we can still expect some form of reinforcements to be placed just to be safe.

Industry & Trade

It was also quite a manufacturing city, as it provided most of the weaponry used by the many hundreds of thousands of troops used by both men and elves during the Last Alliance. Due to its position, travel across the Misty Mountains primarily passed through Rivendell.

Assets

It appears to boast a decent library and museum. Narsil among other important artifacts were held on display in Rivendell. Many also appear to have come to Rivendell seeking knowledge and there were the last surviving documents from Númenor. Much of the elven history was preserved there too. It developed a reputation as a valuable destination for all those seeking quality advise and to learn history. Essentially the key to elven soft power.

History

The elves spent the opening phases of the War of the Elves and Sauron getting pretty soundly defeated. The sacking of a major elven kingdom outside Moria led many to flee. They settled in what became Rivendell. During the Last Alliance, Rivendell became a major base for military preparations that later became essential for victory. But Gil-galad died in the battle, leaving Elrond as the head of state. After this point, Rivendell continued to be allied with both Moria and Arnor until both fell. The Witch King was able to eventually destroy Arnor, but due to in part Rivendell was in turn driven from the area. Once Moria fell to the Balrog, Rivendell became geopolitically isolated - no major military powers to either ally with or be threatened by.

Geography

The position made it vital in the history of Middle Earth. First, many elven refugees formed its original citizens, which then went on to strongly resist Sauron's advances in the War of Elves and Sauron. Its position also allowed it to play a role in defeating the Witch King by sending timely reinforcements. Both Thorin’s company and the Fellowship left from there. Thus, we can assume that it controlled a vital place on the Misty Mountains.
Rivendell has a coniferous forest surrounding it. It also appears to be extremely difficult to get to – most entrance and exit points require single file travel along very treacherous mountain passes. There are apparently less difficult ones to use, but not even Gandalf was aware of them prior to the events of the Hobbit. The climate is described as semi continental with moderate temperatures and rainfall.

Natural Resources

Now, one of the major weaknesses of Rivendell is that it lacks much in the way of farm land. As far as I can tell, there is one garden. So it is possible that some food is produced here. But mountains are not known for being the most fertile areas. Now valleys with gentle rivers are another ball game. So while some food production seems logical, it would not be as solid on this front at other elven kingdoms. The down side is that an outright invasion would not be needed if access to the outside world can be cut off. Perhaps a few solid raids would all that it would take.

Type

City

Location under

Misty Mountains

Owning Organization

Elven Governments