We had a great time staying in Simone's apartment. We walked everywhere (including to/from the train station) and never got tired of the city.
There is a great little square down below where we enjoyed coffee, daily aperitif and some AMAZING gelato (fresh made daily for only 1 euro/scoop!). Ponte Vecchio is just down the street (great pictures) and Piazzale Michelangelo is a 15min walk (great view over the city).
The apartment was tidy and quiet (there is some street noise in the evening but nothing too loud) and was very nice to come back to each day. Would recommend to our friends!