I was visiting Florence for 4 days with my mother, who is very neat and therefore difficult to please when it comes to cleanliness. She was pleasantly surprised by how clean Patrizia's apartment was! It's spacey and equipped with everything you need to stay cool, clean, well-rested and well-fed (except for a kitchen knife - do correct me if I am wrong; we figured it was missing for safety reasons). We weren't missing anything while staying there, and the beds were both very comfortable. We never met Patrizia in person but she was quick to respond to any queries we had, and even sent someone to arrange the sofa bed within less than a day. The wifi connection is flawless and the flat is protected by 3 separate doors.
The area is just the right amount of "local" and quiet, detached from the bustle of the center but still within a walkable distance. There are small grocery stores, restaurants and beautiful churches in the immediate vicinity. Crossing any one of the bridges of the Arno to get to the "touristy" center, including the train station, will take 15 minutes on foot. Unless you have any particular reason to be sleeping within a crawling distance of the Duomo or SMN station, I highly recommend staying at Patrizia's flat!