We had a very nice stay at this B&B located in the centre of the old city, 300 metres away from the Vatican. The room was nice and clean. Everything you need for a short stay in the city was present. It was also located in a quiet area. The breakfast was simple but lush by Roman standards, with some variation (self made cake, croissants, ...) We stayed here for 7 days, every time we returned we felt at home. We could relax from a long day of walking. The host was discrete and helpful.
Internet access would have been nice, because mobile coverage was not so good. But there are plenty of restaurants, bars, ... with "free" wifi.