I've been to Rome, but have no experience there on a bike. I did spend two weeks in Florence and used a bicycle. Rome is more narrow and congested, but I found that aspect of Florence to be an asset. It slows the cars down. Use public transport if you have to go through too many crazy areas, a folder is a great idea. Learn the alleys, they are the way to go, and snake absolutely everywhere. Boston and NYC are trials by fire themselves, you'll be fine and fluent in a whole new cornucopia of hand gestures 48 hours after the jet lag wears off.
--A