We had a lovely stay at Lorenzo's flat and just loved the rooftop terrace and the location of the flat in general (20 min walk to the Duomo, etc). The only "problem" we had was that one of the beds was not prepared and we spend a few minutes looking for everything and had to make it ourselves. However the aircon and the view from the terrace was just perfect. All together the flat completed our stay in Florence and made it a wonderful experience.
P.S. Make sure you check out the ice cream parlor (B.Ice) just around the corner, which has very good ice cream and some lovely owners.