In Rome I have stayed at Dei Mellini, on the other side of the Tevere river but very well located. It´s a 4 star but we found it gives reasonable rates off-season.

This year however, we will stay at Hotel Ponte Sisto, very close to Campo De' Fiori. This is a wonderful location. The hotel gets very good reviews in Tripadvisor. The rates offered directly by the hotel are high but I found a booking agency in Italy ( recommended in Tripadvisor and Fodors) which booked us the rooms much cheaper( I think it was close to 50% off!). I believe the website of the agency ( and there it has links to hotel information) is www.reservationitaly.com.

I'm sorry I can't provide the links to the hotels or agency as I'm in Puerto Rico and can't access my favorites.