if you're looking for a quiet place in Rome that's close to all the sites I'd highly recommend Vera's apartment.
The apartment is close to the river and well connected to local transport - but you can walk to most places within about 20 minutes.
Vera is easy to communicate with if you need anything. We booked our stay on the day of check-in and she got in touch immediately to arrange to meet us and let us into the apartment within a couple of hours. She also provides a massive book of local tips that were very useful for ideas of things to do and places to eat!