Chiara & Lucia's Trastevere apartment is, indeed, as nice as everyone says it is. They have thought of everything you might need and more. The area is very busy night and day, but the apartment faces a quiet courtyard and you hear almost nothing. In fact, you should set an alarm or you might snooze the day away, especially if jetlagged.
A favorite local place for us was Pianostrada, just around the corner. Very small place, creative and delicious sandwiches, salads, and everything else. Not a restaurant, but street food done with flair and great ingredients. Limited seating but worth the short wait.