For me, Alderighi's apartment is what Airbnb is all about!
Alderighi is a genuine Italian gentleman who carried my bags up the stairs to the apartment (although the stairs aren't that bad anyway). The flat is a charming, quirky and interesting space, very comfortable, and the roof garden is brilliant for breakfast in the morning or drinks before heading out for dinner.
It's perfectly situated very centrally but also feels less touristy when you explore the Santa Croce area.
If you want to feel like you actually live in Florence while you stay here, then this apartment is perfect.