I second the recommendation for Hotel Delle Nazioni. It is a stone's throw from the Trevi Fountain. We have stayed there a few times, most recently in Feb. We stayed in rm 504, which is quite small but opened up to our own private rooftop terrace! Incidently, one of the Mgr's is a friend of ours and just spent his holiday with us here. He was pleased to see the recommmendation posted here. One note of caution, they are SLOWLY undergoing renovations, so the lower floors may not be available.
Editing to add, pricing should be in the lower-mid $200 range - depending on season, of course. Winter & shoulder season they were offering a 4th night free. I think it averaged out to right at $200 nightly. Excellent price for City Center.