Casa de Fico
My husband and I spent four nights at Casa de Fico and were very happy with our choice.
Pros: The best features of the apartment are that it is very central to historic rome sights, it sits on a lively little piazza, and it has great light and ventilation. It was HOT when we stayed, but we didn't need the air conditioning at all. There is also a washing machine, which is great if you're on a longer journey. The host, Marcella, was very accommodating to our slightly early arrival time. Other than the initial meeting, this was a very hands off stay, a pro for self-sufficient travelers, perhaps a con if you like more direct engagement with a host for recommendations, insights, etc.
The bar/cafe downstairs was perfect for a morning espresso and early evening drink. Da Francesco, also on Piazza de Fico, had good food for reasonable prices and didn't seem as touristy as some of the surrounding options.
Cons: The cafe/bar in Piazza de Fico is quite loud through 3-4 am all nights. Shutting the windows only partially blocks the noise. With earplugs, I had no trouble sleeping though a more temperamental sleeper could have issues, especially in the summer months when the crowds outside are in full force.