I've been shooting a D7000 now for a few weeks, and quickly learned the consumer zoom I was using on a D80 wouldn't work on the D7000, unless I was happy with two D80's
(Except one of the D80's being waay faster and sweeter!)
Most of the time a Nikon 50mm 1.8 has been on the camera. The D7000 is now able to show the tack-sharp detail and clarity it's capable of. You can find this lens at Adorama or B&H for around $125 (!), so you might want to start there. Of course, on APS-C it's approx 75mm, but you may find that useful. Just try to shoot it at f/5.6 thru f/8, if you get one. Btw, all these people complaining on forums that they can't get a sharp picture from their D7000's...most gotta be doing something wrong. Nikon couldn't have let that many bad cameras slip through quality control.
As for zooms, I'm in the same position as you. The Nikon 16-85 zoom has a reputation for being one of the sharpest DX zooms, and the price is not too terrible. But once you see what a prime can do for this camera, you'll want to put the best glass on it, which is why I'm also considering the Nikon 24-70. That lens has near-prime resolution, and is much less expensive than buying the several Nikon or Zeiss primes you'd need to cover the same range. Plus, if you ever go full-frame, well, there ya go.
You could get a Nikon 35mm dx prime, plus a Sigma 105mm macro or 150mm macro prime that would be within your $1000 budget. They are supposed to be sharp, according to many users and reviews. Good luck and good shooting!