My mother and I spent a very comfortable 5 days in Christina and Gianni's flat in Florence. The flat is located in a quiet street on the edge of the historical centre, meaning that we could escape the throngs to a more authentic. It is surrounded by small shops and restaurants it is just a 15 minute walk to the Piazza San Marco. Alternatively, there is a bus stop less than 30 metres from the flat, with regular buses going to the centre and train station.
Christina and Gianna are lovely people who were nothing but helpful from the moment we booked the apartment until the morning we left. They are passionate about their city and have lists of recommendations for eating, sightseeing, cultural and historical visits, etc. I would not hesitate to return the next time I am in town!