Stefano's apartment location is perfect to explore Florence. You can walk everywhere you need to in the city yet still have an amazing neighborhood and nightlife right downstairs. We didn't have any issues with the noise in the square at all during our weekend.
The elevator was great to have for our bags but we took the 5 floors of stairs otherwise for some exercise (don't forget to close both of the elevator doors all the way when you get out, otherwise the elevator won't move when the residents call it).
The balcony is by far the best place in the city to get a pizza takeaway and a few drinks and watch the sunset with the Duomo and the piazza below lit up. Definitely recommend finding an excuse to hang out there during your stay. Recommend Konnibio and La Menagerie for dinner and lunch, as well as Ditta Artigianale for excellent coffee and breakfast.
The apartment is otherwise well appointed, good AC, nice finishes, comfy bed.
Pro-tip: Buy a Firenze Pass and climb the Belltower instead of the Duomo. The views are still amazing (esp looking out at the Duomo right next to you), you can go right to the front of the line (skip the line at Uffizi and Accademia as well!) and it is not a bad hike if you're in decent shape with multiple landings/lookouts on the way up to rest. Worth every penny.