Napoleon Hotel - we stayed there for 3 nights a week ago and it was great! Right next to the Metro which is a big thing if you are planning on move all around Rome.
I stayed at Hotel Dorica on a friend's recommendation a few years ago and it was great. Clean, nice staff, centrally located. I think I only took public transportation to get to and from the airport. I was able to walk everywhere else, but I'm a big walker in general.
Hotel Raffaello in the neighborhood near Termini is very convenient to many restaurants and sites. It's very near some great churches, about a 15 minute walk to the Forum/Colosseum area, and 20 minutes to the Pantheon. Decent breakfast and friendly staff.
Hotel Farnese is on the other side of the river, about a 15 minute walk from the Vatican. Very lovely decor, spacious rooms, great breakfast, very friendly staff, and modestly priced.