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I'm no expert but i could see a few reasons why it wouldnt work. The main reason being the insane amount of stresses the building would face. It would have to deal with things like wind. Gravity would probably be too much for it, the intense weight of the building would crush it. The centrifugal forces wouldnt help it i think, and would only make the stresses even worse. The portion of building at the center of the gravity/centrifugal tug-of-war would want to tear itself apart. Something like a small earthquake would probably also be devistating. Also imagine if something were to happen that would require the building to be demolished or taken apart (or if it fell apart), it would be extremely dangerous to people over a huge swath of area.
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.
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