I can't emphasize enough how much time and money you save by being close to the tourist attractions,

Once you know which area/areas you would like to stay in how do you find the best price? Aha! This is my area of expertise. My page on tripadvisor.com explains what TripAdvisor is and how you can get the most out of this Hotel search tool.
If you are thinking about staying outside of the city center you may want to reconsider. In my experience the advantages of staying close to the Rome tourist attractions and nightlife far outweigh staying in the suburbs.
I can't emphasize holiday car rental enough how much time and money you save by being close to the tourist attractions, monuments, restaurants, holiday car rental nightlife holiday car rental etc. It's also true that one's experience of Roman life and culture can vary greatly depending on which area of Rome you stay in.
April, May, June, September and October (and also Christmas, New year and Easter) are considered high season holiday car rental by most hotels in Rome. Bearing in mind July and August are when Italians migrate to the coast.
Of what does breakfast consist? Fruit, cereals, cold meats, holiday car rental bacon and eggs? (Remember that a Romans breakfast usually consists of an Espresso and a Croissant.) It's true, however, that breakfast in Roman hotels is improving after decades of grumbling foreigner's tummies!