First, big thanks to Lorenzo for the recommendations and information! He was very helpful and fast in responding.
Lorenzo's place was also great! It is a cozy, newly remodeled apartment in an old and well kept building that can be good for 3 people, just maybe no small kids. It is very stylish and very very comfortable. The photos don't do it justice! It also has an a/c which made all the difference for us! The location is perfect. An easy 5 minute walk to great restaurants and a 10 minute walk to the sights, but away from the crowds. It's in lively Piazza Santo Spirito which is like East Village in New York, but facing back so it was very quiet when we were sleeping. Sunny during the day. Pretty view of the hills and a private rooftop garden. We would definitely come back.