The Hotel Alimandi near the Vatican is a wonderful hotel and is priced reasonably. The only downside is that it is a 15 minute subway ride to the downtown area (Spanish Steps, Trevi Fountain, etc.), but the Vatican is right next door. We stayed there for five nights in August, if I recall, a double is 100ish EUR a night in the off season. It is run by a family and they do a fantastic job. They also have a complimentary shuttle to and from FCO.