I absolutely recommend Maison San Lolo appartments. Me and mom spent 9 days in Rome and were very happy that we chose it. Andrea is very nice host, even though a little bit oblivious :) He warmly welcomed us at the first day, despite our quite late arriving. Andrea is always ready to help and easy going person.
The house is located in good area: yes, it is near Termini station, but far from "looks like criminal" part of area. Near you could find lots of cafés / bars / trattorias to eat, or supermarkets to cook at home if you want to or on some diet - the kitchen has all necessary equipment. By the way, you can easily reach bustling bars, but they are not too close to disturb your sleep. But if you have problems with sleeping, or you need soundproof bunker for it, you may be disturbed with emergency cars, since the hospital is in the area. But frankly speaking, I hadn't such problems except the very first morning.
If you like hiking, you can go to the city centre by foot: we did so almost every day - it takes about 40 minutes to get to Piazza Venezia, for example. Or you can use public transport.
As for apartments, they are lovely as on photos: neat and beautiful. I slept on sofa for more than a week, and it was quite comfy. The bathroom is equipped with shower cabin, some people may find it small..... But we hadn't this problem.
We are very satisfied with San Lolo appartments!