It all depends what you are interested in photographing and thus what type of lens you are interested in.
There are a few zooms in that price range, example 18-55 Nikon, 18-70 Nikon, 18-105 Nikon. These kit zooms are better than they get credit for. Longer zooms are also available, ex: 55-200, 55-300 from Nikon. These are not the top of the line pro models with constant apertures, but for the money, they are pretty good.
Nikon offers quite a few primes in your price range as well. 28 2.8, 35 1.8, 35 2.0, 40 2.8, 50 1.4, and the ever popular 50 1.8.
Throw in third party and second hand offerings and the choices become practically unlimited. Your D7000 can autofocus with nearly every auto-focus ever made for nikon (except for a few very rare lenses made for F3). Your D7000 can also meter with nearly all Ai and Ai-s ever made.
Good luck in your search. Give more details of your requirements and folks will be able to give you more specific recommendations. No matter what is said though, the final choice is yours and yours alone, and that is as it should be.
For me, I would recommend a prime, say a 50 1.8, simple, fast, small and spectacular sharpness. It is the cheapest clear lens there is for me! But like Patrice said, need to provide more info, if you primarily shoot landscapes, this would not be a good choice!
You have to let us know what you're shooting....lighting conditions & focal lengths differ in every shooting environment so we can't tell you what exactly is a good lens for under $400 if we don't know what you're shooting.
If you like primes, I personally have always loved the 85mm f/1.8D on my D7000. I've gotten amazing photos from that lens. And as always for any camera, the 50mm f/1.8D lens will give great results, and at a low price; or you can get a little more light & bokeh out of the 50mm f/1.4D which is still under $400.