We had a great stay at Lucias place. We had a garden (which was shared I think) to ourselves whenever we needed it (with a bbq) and the studio was air conditioned which was perfect, especially for our dog!
It was located 5 mins walk from the bus which can get you into the centre of Florence in 10/15 minutes. There are a few good restaurants nearby. We really enjoyed Calino (seafood restaurant)
Lucia was a great host and very accommodating and gave us lots of recommendations. It was perfect for a stay in florence with a dog!!!