We had a great stay at Magguy's flat. It's located near Termini so it's convenient if you need to take the tube or a train to go outside Roma, but most of the time we walked.
The building is in a nice area (really good coffee at the bar in front of the building), not really touristic though.
The flat is really spacious with a high celling and 2 bedrooms, and it's really quiet!
I would definitely recommend Magguy's flat.