Trastevere is a great location. It's full of both tourists and locals that come to that area nightly. Not totally in the City Centre, but just a 10 minute walk from it. Restaurants are awesome. We recommend Tonnarello and their cacio e pepe and carciofi alla giudia! The apartment itself was a great place to recharge in-between adventures and explorations.
Like others have mentioned, the ceiling is low in certain parts, so depending on your height, mind your head as you walk about. I'm 5' 11" and had to duck in two places in the apartment. Standing in the shower was just right for me, so I can imagine someone 6' ft or taller will have a bad time here. Anyone under 5' 7" will be right at home.
Also, as others have mentioned, noise can be an issue. In the living room, it's definitely audible. We'd rate it a 5 out of 10. However, in the bedroom with the door close, it was a 1 out of 10. So take that for what it's worth. It didn't bother us, but I can see how it might bother others.
All in all, it was a great place to call basecamp.