We loved Liviana's place. It is a private room in an Italian apartment which was super cute. The wifi was strong and the breakfast (croissant + cappuccino at a local cafe) was just a few minutes walk away.
Note: lack of AC is not an issue. We stayed at Liviana's place in late August when it was 30+ degrees in Rome. The room we stayed in was super breezy (cross breeze from multiple windows) and therefore the heat was no trouble at all.