Robert - Just a suggestion: rather than buying the 18-200, why not consider a 16-85 AND a 70-300? You'll appreciate that extra 2mm at the wide end, believe me. The 18-200 is an alternative if you're buying just one lens, but I think you'll get more bang for buck with this combo.
I traveled in France this past summer and took a 16-85 and 70-300, as well as a fast 35 f/1.8. After sorting through my shots, I found that I used the 16-85 for about 80% of them.
You can find both of these lenses used for about $500 (16-85) and $375-ish (70-300). A lot of Nikonians are selling their DX lenses as they move up to full frame (although the 70-300) is an FX lens).
I recently sold my 70-300 to a local fellow, and I'll be advertising my 16-85 on the Sell Forum as soon as I can shoot some pics of it. (I also have a 17-55, which is my favorite lens, as well as a 70-200 and a 300 f/4.) Most of the time, I'm working out the car, so having a lightweight kit isn't that important to me right now.
I don't mean to sound self-serving. I just thought I'd throw out an idea for you to consider.
Good luck with the D7100 and let us know how you like it!