The apartment worked very well for us. It was very quiet, shared with a single friendly lodger that we hardly saw; most of the time you have the whole place to yourself.
It has a simple layout, with a kitchen and bathroom at one end of a corridor, and a good sized bedroom at the other. The bedroom has a lovely large bed, a big wardrobe, two armchairs, and a good rooftop view of the city — slightly less 'close up' than the photo suggests, but still worth having! There's a balcony by the kitchen with a small table for breakfast, and a view of the hills outside Florence. A charming old lift takes you up and down.
Beatrice took good care of us, leaving very nice coffee for the espresso machine, a bottle of wine, and some small croissants for our first morning.
The flat isn't on the most beautiful street, but the nearby area is quiet and quickly pretty, with shady old streets by the university and the Four Seasons hotel (there's a 'secret garden' just opposite the hotel entrance...). You'll also find an old Florentine graveyard on your way, now functioning as a traffic roundabout. After just 15 minutes walk through the quiet streets you're in the bustling centre.
If you want something without fuss, and away from the tourist hustle, do stay.