We had a wonderful time at Matteo's apartment. The location is perfect -- extremely central, but quiet -- and we absolutely loved the terraces. We sat on the terrace with our coffee/tea each morning. The apartment appears to have been recently renovated, with beautiful tiles and many nice touches. The bedrooms are large and well appointed. There was good coffee/tea and the kitchen was well equipped. One of the big selling points for us was the elevator which was super convenient for carrying our luggage to/from the apartment.
Matteo was a fabulous host. Anytime we had a question as we were planning the trip, when we arrived, as we were preparing to leave, etc. he got back to us within the hour, often sooner. We arrived a bit early into Florence and he was very accommodating in allowing us to store our luggage and then letting us know when the apartment was ready.
As a previous reviewer wrote, there isn't really a "living room" -- there is a sofa in the entry way and sofa/loveseat in another small room off the terrace, but not a place indoors where 4+ people can gather easily. It was just two of us and any sitting around was done on the breathtaking terrace, so it was absolutely fine for us, but good to know if you've got a larger group.
We are thrilled with our decision to stay at Matteo's apartment and highly recommend it.