You will get mixed reviews on the 18-105 vs 16-85 question, having used/owned both on my D7000, I did feel that the 16-85 was cleaner, less distortion, and sharper, others say the difference, if any is minimal. Either way, I felt it was the best walk around lens (for me) and delivered all the performance I needed without any complaints.
You didn't say anything about budget, but another option is if you are looking for at a 10-24 would be to grab a 24-120 f/4. It's an FX lens so it's much fatter and heavier then the DX lenses listed above, but will deliver an equivalent focal length of 36-180mm with a consent aperture. I borrowed one for a week and was very happy with the results with a few caveats. 36mm isn't that wide and I didn't have anything wider with me so there were a few shots I just couldn't get. Also, have I mentioned that this lens is heavy compared to say the 16-85 by a 1/2lb? Bright side, if/when you move from DX to FX you already have a great walk around lens.
Just something else the chew on. Best of luck in your search.