Originally Posted by ObieX

The reason a space elevator would work so well is that it would be more like a tether, like a super-strong wire. It would be vastly more flexible, and able to stand up to much more stress than a building would.

On the other hand if you want to look at your idea in a slightly more limited way, you could place a structure at the top of the space elevator. Sort of a starwars cloud city, only in space. The main draw of this idea is probably the space elevator itself and ease of transport tot he "building". I dunno how large this structure could be, comes down to a lot of stuff like how you would anchor something like that, and what kind of tethers you could use to support such a large mass.