If you are considering the 18-70mm, you may want to confirm that it has a weather-sealed mount, and see if your other contenders are similarly sealed, as the D7000 has some level of weather-sealing. (My wife has an 18-70mm, and I think it has a gasketed mount.) I do not think, however, she has used the 18-70mm on her D7000, so I cannot comment on how it performs on a 16 MP camera. It seems to do well enough on a 6 MP D70s.
Canon 7D2/7D/5D/40D/1D2N/M3; Nikon F6/D700/FM3A/1Dx/Coolpix A; Canon 40mm 2.8 STM, 135L, 50L, 35L, 50mm 1.8 I, 100mm 2.8L Macro, 10-22mm EF-S, 400mm 5.6L; Nikkor 50mm 1.2 AI-S, 50mm 1.4G, 50mm 1.8D, 16mm 2.8D Fisheye, 180mm 2.8D, 100-300mm 5.6 AI-S, 18mm 2.8D, 45mm 2.8 AI-P, 14-24mm 2.8G, 24-70mm 2.8G, Micro-Nikkor 60/2.8G; Voigtlander 90mm f/3.5 SL II