Gaia's flat was great: clean, stylish, spacious with a great view.
We loved that it was so close to the airport bus stop and everything we did was within reasonable walking distance, some really close by like the central market, the historic center and great gelati places (try La Carraia and B-Ice!).
On the other side of the church Santa Maria Novella there is a tourist info point where luggage can be left on the last day, that was really convenient if you compare with the queue at the train station. We could checkin early and leave our luggage in the morning upon arrival, that was cool.
Also great was the air conditioning - it was well above 30° when we stayed. Great place, really!
One thing: flat is on 4th floor so if your legs aren't what they used to it might not suit you so much but it wasn't an issue at all for our small party of 50+ even after a day out walking - coming back to the flat was a reward!