My wife and I stayed at Diana's place during our honeymoon and you'd be hard-pressed to find a nicer place if roof-top, sitting enjoying panoramic views of the city with a glass of local wine in your hand is your idea of a good time. Located in the Oltrarno area of Florence (opposite side of river from many major sites), it is a 25min walk from the train station, 20min walk from Galleria Academia, 15min walk from the Duomo and palazzo vecchio, and 10min walk from Uffizi Gallery. It is located in a residential area which has fewer hordes of tourists than on the other bank of the river which is pleasant.
A smaller apartment, the rooftop terrace is the highlight. There is a table with 6 chairs as well as an additional 2 sunbathing chairs. It offers unparalleled views of the city, 180deg. The buildings to the west begin providing shade around 1-2pm which is nice as to not bake in the sun. It's great for watching the sunset over the city. There is a steep climb up a hill to the apartment itself and then typically Italian stair-steepness to reach the 3rd and top floor for the apt.
We'd recommend this to anyone looking to stay in a place somewhat away from the crowds while offering a wonderful venue for enjoying a book, glass of wine, appertivo, and fantastic views of the city!