We loved Firenze and were very happy in Fabrizio’s place. I would suggest using the T1 tram from SN train station to his house especially with luggage. It still involves some walking but it is flatter and much easier than the uneven surface or hills encountered if you just follow walking directions. You can get tram ticket at tram stop. Don’t forget to validate tram ticket at the yellow machine once you are on tram.
Getting around Florence was very easy and walkable once you were at SN Train Station. Also Rick Stevens’s free audio tour “Renaissance Walking Tour of Florence” gives you a great overview/history of city. We would stay at Fabrizio’s place without reservation when next in Firenze!