A very nice studio apartment in San Lorenzo - Termini is a 15 min walk away, and the neighbourhood is lively (in a positive sense), with many bakeries, bars, restaurants, all if which are a lot cheaper than in central Rome. NB: I walked home from a concert nearby at 23:00, and it was perfectly safe and calm.
Federico was a very thoughtful and responsive host, and I had a very good experience in the apartment.