Hi Kathy,
I shoot a D7100 and was also looking for something better than the 18-105 mm kit lens that came with my D90, both of which are now in the hands of my niece. I bought full frame to cover the long end and beyond and was going to do the same for the wide, until I read about the Sigma 18-35 mm f/1.8 ART lens, designed for crop sensors. Twice your budget, I'm afraid, but half the cost of the full-frame Nikon I was considering, and I have to say I love, love, love it. It is very well reviewed and I have found it a delight to use. It is very sharp corner to corner, conserves the 1.8 focal length throughout the range, has nice heft and feels very solid and well-made. It has been on the market long enough that there are used copies available, so if there is any chance you can stretch your budget, I am pretty confident it would not disappoint you. Apologies if this is not useful to you, given the cost consideration, but there may be others who might be interested in the endorsement, not to mention the fact that it is by far DXOMark's highest rated standard zoom for the D7100 (see
here).
Edit: I should also add my endorsement of the very inexpensive Nikkor 50 mm f/1.8 prime. It was my second lens and has never disappointed me.
And the Sigma has very nearly made my Nikkor 35 mm redundant. I have not let it go in case I might want to use it for panoramas, but the fact is, I have not used it since I got the Sigma.