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I've used the Tokina 12-24 f4 for years and last year bought a D7000 to use with it and it worked well, so I can recommend the Tokina's for sure. They are solid lenses and built well and although I haven't handled the Nikon 10-24 or Sigmas, I'd rather have a solid lens than a light plastic one (all may be very solid and well built but I don't know). Tokina does have CA wide open when doing astro shots, but the others may do as well.
From what I've read the Tokina 12-24 performs about the same as Nikon's 12-24 f4, but at half the cost.
You've probably read about this so apologies if I'm repeating. For the lenses that you listed however, keep in mind the range of the zoom. 11-16 isn't much of a range whereas 10-20 or 10-24 will give you a bit more versatility and saves changing lenses if you need something slightly higher than 16mm. Having said that the D7000 images can be cropped quite well still if shot at 16mm if you need to zoom in.
The advantage of the Tokina 11-16 is that it is constant f2.8 which is an advantage for astro shots. Also it's sweet spot would probably sit lower in the range than an f4 lens (probably about f5.6), where it's at it's sharpest and lowest CA.
And of course there's the cost... Nikon's are more expensive than the other two so if that's a factor go with Tokina or Sigma - they're both good.
I've now bought a D800E so I have two cameras now, and also the Nikon 14-24 f2.8 FX lens which is THE best wide zoom, but on DX it's cropped and would be 21-36mm equivalent. Upgrade to an FX camera if you can afford it! haha.
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