You didn't say which zoom range you'd be most interested in, but you have plenty of options.
The Nikon 16-85 (and presumably the new 16-80), 10-24 and the 18-140 suggested by the previous post are all fine DX lenses for your D7100.
You may also consider the 70-300 by Nikon. While it is technically an FX lens, it gives very good results with a DX, and in my opinion, is a lot of bang for the buck.
There won't be much of an advantage to buying FX instead of DX if you can find what you need as a DX offering. On the other hand, I don't shy away from buying FX lenses for my D7000 when they suit my needs better than the current DX offerings. (The 70-300 and 80-400 are two examples).