If you want the most authentic Italian experience, i recommend you to stay in this apartment. The neighborhood is amazing, and it is known for great restaurants, small handcraft shops and wine bars. Every day there is a small market in the piazza close to the apartment called Santa Spirito. In the street right outside the main door, there is a cafe, on the other side of the street there is a charming wine bar with lots of craft beers called "Tuscan taste florence", and here we took a cooking class that was gluten free and amazing (they have normal ones too and wine tastings). The most amazing thing about the apartment was that it was so close to everything, you can easily walk to the centre in 15 minutes and to the grocery store in 10.
We stayed here for a month and it was really charming and functional. For an Italian bathroom this was high standard, and there was no mould which is rare here. The bed was comfortable and there was a large sink, so it was easy to wash the dishes. The french balcony was very charming, and the apartment has very high ceilings and big windows so it feels bigger than it is. You also get the sun in the afternoon and evening!
Lucia was very helpful and friendly, and checked up on us during our stay. She was very punctual and helped us order a taxi when we left.
The only thing to note is that the toilet room has a door that does not properly close, so stay here with someone you are comfortable with :)
All in all, i would totally recommend this place. We have been to Florence before, but to live here on the other side of the river with so much happening around us, was an amazing way to fall in love with the city!