I highly recommend staying at Andrea and Mery's apartment in Trastevere. It was a good size and very clean.
The neighborhood is fantastic, a perfect mix of local feel and activity. It was away from all the tourist heavy parts of Rome but never too far to get to anything. Great cafe's, bars and food around. Lots of options for groceries, laundry, pharmacies if needed. It is near the main street in Trastevere but off of it so nice and quiet at night when you're trying to sleep.