We had a really pleasant two nights at Hotel Grifo. It was one of the best hotels we stayed in during our two week trip to Italy, and not the most expensive by any means.
The hotel is well positioned to explore the historic "east bank" of the Tiber on foot. We booked a tour with pickup transport for the Vatican, which was worthwhile. The hotel is close to buses and the underground, but we didn't use either.
In particular the staff were very helpful with advice and bookings.
The breakfast was great too!