I often use AirB&B, and this location is definitely one of the best I've stayed at. The place is bigger than I expected and is very nicely decorated. Additionally, you find everything in the house to make yourself at home and the view from the kitchen while sipping in my morning coffee was awesome.
The place is 20 min walk from some of the best attractions in Florence, but far enough to find genuine shops and people.
Unfortunately, the fridge was not working when I stayed in the apartment, so that was a nuisance, but I guess that it has been fixed.
Definitely would stay back at Barbara's place when in Florence.