Though I'd probably say the D7000's JPEG photos are clean up through only ISO 800, they remain very good through ISO 1,600. By ISO 3,200, shadow detail gets pretty noisy (look at the text in the shadow under the currency).
Noise, raw vs. JPEG, ISO 6,400
I've found that you can eke out at least a stop more of usability out the the D7000's medium-high ISO sensitivities by using raw instead of JPEGs. (This is a quick-and-dirty version. I could probably get some better results.) Granted, the images aren't noise-free, but the monochrome-grain appearance is more attractive than the in-camera err-on-the-side-of-color noise approach, and there seems to be enough dynamic range that there's still shadow detail and little loss of sharpness. (1/125 sec, f2.5, spot metering, AWB, Neutral picture control, 35mm lens)
Distortion, 24-120mm lens
At its widest, the 24-120mm lens has a little bit of symmetrical distortion (look at the curvature of the top horizontal lines), but nothing atypical for that focal length.
Picture Control settings
Nikon pushes the saturation a bit in its default Standard picture control setting, but it doesn't display the wholesale color shifts we tend to see on lower-end models. However, as you can see when you compare the Neutral setting with all the others, it does push the contrast to the point where you lose quite a bit of shadow detail. (1/100 sec, f4, ISO 200, AWB, evaluative metering, 24-120mm lens at 86mm)
The D7000 has very good color accuracy and saturation.
24-120mm f4 lens
I shot mostly with the 24-120mm lens and was quite happy with it. The bokeh is very nice, and the lens is sharp, bright, solidly built, and comfortable to operate. (1/100 sec, f4, ISO 200, evaluative metering, AWB, 24-120mm lens at 65mm)