Vincenza is definitively a host I would recommend, kind, very polite and helpful. :-)
The flat is located in a residential district, 10 min by taxi from the airport, 3,5 kilometers from Firenze Santa Maria Novella, the main railway station and 4 kilometers from the dome of Florence. Most of the city center is closed to traffic, so you better walk 5 min on foot up to the tram stop and hop on the T1, which will take you directly to the main railway station in just in 5 min.
And if you like parks, you can walk for 300 meters up to the river Arno and cross the bridge that leads to a huge park called "Parco delle Cascine".
The flat itself is nice and comfortable and it also appears as it has been recently renovated. The sleeping room is spacious and cosy. It also has air conditioning, which is extremely helpful, since it's usually very hot in the summer and sleeping with the open window might be a problem, if you are not used to the the noise coming up from the street.