I highly recommend Claudio & Pat's apartment in Prati. It has been one of my favourites while travelling Europe the last couple of months.
The apartment is very well located, only two blocks from the metro (you can get from the apartment to Termini in less than 15 mins) but also only about 10/15 mins walk from the Vatican. The street it's on is pleasant, with small cafes and bars to drop into.
The apartment itself is ideal, it has everything you need and is very well laid out. I think it is much better in person than in the pictures. The washing machine, oven, stove, shower etc all work very well. The TV has netflix on it if you're spending some time in the flat.
Claudio & Pat's communication was quick and very friendly throughout. Overall I highly recommend staying here if you're visiting Rome.