We have been very happy with the Air B&B managed by Anthony. The AirB&B by itself and its location is very impressive. We were five guests for one week, and felt very comfortable. We felt independent and had our meals all together. The apartment has a feel of a very old town place, but not outdated with a powerful wifi and really great beds. The place's kitchen has a large variety pots and pans, enough to host meals at home when the restaurants are too busy.
The location is amazing: 5-10mins to all major sites. The old city is pretty small and walk-able, and the apartment is right in the center of it. We never needed to take the bus, nether have a car.
Anthony is a very nice and helpful host. He gave us some interesting addresses and described the apartments very well! All our exchanges were courteous and friendly.
That was our first time in Florence, we warmly recommend this place.