I was in Rome a couple of years ago and the 17-40 should be good for most of what you would like to photograph. I used my 18-55IS and it worked fine for most stuff.
It wasn't wide enough in the Coliseum and the Diocletian baths. There are some places where a wider lens would be helpful. I picked up a Tokina 12-24 F4 for my next trip.
I like to get shots in museums, and IS is useful here. An alternative would be a shorter, and faster prime, like the 35f2 or 35f1.4.
I recommend bringing a backup lens that will do if you manage to damage your main lens, or if it dies on you on the trip. It happened to me in Rome (I tripped and the lens hit the concrete), and it happened to a friend on a trip to Ireland (decentering).
I'd get a superwide if you can swing it or a fast, shorter prime - this depends on your interests.
Incidentally, I was able to walk to Trastevere from my hotel in the evenings for dinner and sightseeing. I didn't want to drag along an SLR, and a good pocket camera would come in handy for these trips. I carried my wife's point and shoot for these evening walks.
Wider is better in Rome, and a long lens won't be of much help - to my eyes.