There is a lovely B and B called Relais al Senato, on one of the side streets into Piazza Navona that we like to stay at. It's really like a small hotel with private rooms that are all en suite. The bedrooms have hardwood floors and the bathrooms are lovely. Once you check in they give you a key because there is not someone there twenty four hours a day, just during day time hours. They serve capuccino/croissants/fruit in the little breakfast room in the morning.
The location can't be beat, it's literally 10 steps to Piazza Navona. We like to walk to the Vatican from there.