I stayed at Giovanni's place with my mom in early January for 5 nights and it was a very pleasant stay.
Giovanni was very helpful throughout our staying. He readily helped me and my mom lifting the heavy suitcases up the stairs, and was always there in less than 5 minutes when I called to fix some problems we had in the apartment. His place is cozy and well-equipped. Downstairs is a trattoria which gives much heat to the floor, keeping the place warm even in the winter times. The wi-fi signal was rather low, but I had 3G working on my phone so it was not a big deal. The location is perfect, right next to Uffizi gallery and the Piazza Signoria. Also, Ponte Vecchio is 2minute-walk. We arrived at the apartment by taxi from the train station, which cost around 15 euros, however, if with (very)light suitcases, reaching the place by foot would be not so bad.
I would definitely recommend Giovanni's place if your looking for decent apartment that you can feel home in Florence.