My wife and I were in Rome last month too. I have cycled in big cities, including New York and Chicago, but Rome looked more intimidating. Your post has me thinking that we should have rented bikes for a day or two.
Incidentally, we liked Florence a lot more than Rome, and we were in Venice 3 years ago and like it best. We are at point where we no longer are willing to be moving to a new city every 2 or 3 days so we spent a week in each. We did stay just 3 days in Sorrento this trip and 3 in Verona the previous trip, but I recommend a week in larger cities, and taking time to smell the roses.