I took a 16 day trip around italy back in September. I brought my 18-200VR, sigma 10-20mm, and 35mm f2.
The 18-200VR pretty much stayed on my camera for 95% of the time, with the other 5% being with the 10-20mm.
I guess it depends on your shooting style, but for me, the 18mm on a DX camera like yours (mine is a D90) was sufficiently wide for virtually all situations other than when taking photos of trevi fountain and inside the coliseum and the pantheon. Those are the only situations i can think of right now where I felt the 18-200VR was insufficient in obtaining the framing/composition I desired. This is where the 10-20 came in handy for me.
As for low light lenses, I didnt really feel the need for it since the majority of the cathedrals and other famous landmarks, do not allow photography inside anyways.
If you're interested, have a look at my zenfolio site where you can see a bunch of photos I took in Italy. They're not all from Rome, but you get the idea and it should give you a sense of what focal lengths are needed (click on the info tab to see focal length and other exif data).
Honestly, the 18-200VR is truly an invaluable lens for photography when you're traveling and don't want to be swapping lenses. It is probably the one lens I cannot live without... As much crap as people say about the 18-200VR's IQ, I just don't share this sentiment at all. Take a look at some of my photos and decide for yourself... I think whatever faults you see in my photos are attributed to the photographer and not the lens itself.
Here's the direct link:
http://cman.zenfolio.com/p160806070