When we were choosing a place to stay in Rome, our one reservation about booking Stefano's place was that it might be a little too far out of the city centre. We needn't have worried, as it's located in a quiet and pleasant residential district, with shops and amenities nearby. Although we did walk there initially from Termini Station, this was a long walk, albeit a great introduction to the city, passing through Piazza Venezia and Trastevere. Once we had sussed the public transport system it was easy, especially with a Roma Pass. The 44 bus leaves from the square right outside the apartment and takes you straight to Teatro di Marcello around the corner from Piazza Venezia, from where there are several options to Termini (eg. 64 bus). There is also a bus from the top of the hill (or the other end of the street) which will take you straight to the Vatican, although this is a pleasant walk (20 minutes) through the Gianicolo district with fabulous views of the city (sunrise recommended!)
Stefano's place is perfectly located for visiting the Vatican and Trastevere districts on foot. All the main attractions of the city centre are also within reasonable walking distance, although you might prefer to use public transport to return, as it's a stiff climb back after a day's sightseeing. I'd recommend getting a Roma Pass, as this gives you fast-track entry to attractions such as the Colosseum as well as unlimited travel on public transport. You'll need to add an Omnia Card if you want to include the Vatican attractions.
Stefano was away at the time of our visit, but we were greeted by his brother Fabio, who checked us in, after we changed our arrival time, and who also came early to check us out before our flight home. Thanks Fabio!
Although our stay coincided with a heatwave and the apartment was not equipped with air-con, the electric fans provided some relief and our stay was comfortable. We found the apartment to be equipped with everything you could want and would recommend it highly.