I'd absolutely recommand to go to Betty's. She was a really nice host and we thanks her a lot.
If you need to visit Florence it's totally convenient, everything is close and walkable, you can pretty much go everywhere as you are very well located within the city.
Plus, everything you see in the picture depicts exactly how it is : cozy and welcoming. The flat has very nice furniture and you feel straight away like at home (coffee and tea included!). I'd recommand definetely for some excellent holidays.