If you want to stay 'in the middel of it all', then I can highly recommend Terrazzo Coronari, about 2 min. from Piazza Navona. In a very idyllic alley. The apartment provides you with everything needed and the best part is the terrace. We went in the end of September and it was still warm and nice. Breakfast and evening drinks was enjoyed at the terrace. So lovely :-)
The only thing that bothered me was the bedrooms was very small with sleeping couch and a little 'travel' bed that you need to pull out of the bed. But it worked for us. The apartment is on 5th floor, and there was an old elevator that we could use. In the end we prefered the stairs. But every other thing was just spot on and this is our favorite accommodation in Rome!!