Phobos

Phobos was moved to a position in aerostationary orbit through a mass driver used to recieve shipments from the surface. This, coupled with a couple fusion engines, slowly shifted the orbit to a point where it was feasable to use as the anchorpoint of the beanstalk.
Phobos is one of the smallest objects one can stand on. While the ludicrously low gravity of 0.5 microG, a person can launch themselves into orbit with a jog.
This moon looks like a lumpy potato with a bite taken out of it. In that bite is a large plastic dome, and a series of smaller domes spread over the rest of the surface. The interior has also been heavily carved out for the many millions that live on the moon.