Giancarlo's place is good for a home base while exploring Florence. Though it's on the edge, it's a short walk to the Palazzo Medici and Boboli Gardens, and once you get there, the Ponte Vecchio and museums beyond aren't much more of a walk.
Giancarlo is suuuuper helpful and responsive. He sent us maps of bus lines and how to get from the train station to his place and has a handy laminated guide to the apartment and the city, as well as a full city map on the wall. He also had suggestions for restaurants and places to go to see the city well.
The apartment has a window to the inner courtyard for cool air, but the windows aren't currently screened, so be careful about mosquitoes, especially while you're sleeping.
It's around the corner from a laundromat and a few bakeries for breakfast, and there's a tasty pizzeria near the square.