Luciano and Sabrina's place is a great option for those looking to stay in Florence. The location is amazing, chatting with them helps one get "under the skin" of the local culture better, and their recommendations for what to see, do, and eat are invaluable.
They're also really excellent hosts - very communicative, extremely responsive, and they have a finely-honed instinct about when to engage/not engage with guests who might be looking for a bit more social interaction or peace + quiet :)