Trastevere is a lovely area in itself, but what was ideal (for me, anyway) was how central it was for visiting most of the Roman sites. If, like me, you like walking - always the best way to appreciate a new city - you'll find the big sites (Vatican, Colosseum, Trevi Fountain, Pantheon, Keats-Shelley House, Protestant Cemetery, Spanish Steps etc) within about 30 minutes walk.
Coming from Fiumicino Airport, I got a train to Trastevere Station (every half-hour, takes 30 mins), then bought a BIT ticket (€1.50) at a local shop, and took the No.8 tram to 'Belli' stop (about 7 stops and 7 mins) and Claudia's is a mere 3 minute walk from there.