An absolutely BEAUTIFUL apartment a short 10-15 minute walk from the Florence City Center. Much (all?) of the surrounding apartments are inhabited by the hosts' family, so everyone is extremely kind and friendly. I'd stay for months if I could. There's a cute little turtle nest just outside the flat and some friendly cats as well. Safe for toddlers, and I couldn't have felt more welcomed.
You can walk to the Santa Maria del Fiore Cathedral, Gallerie dell'Accademia, and many other sights. There's a supermarket two blocks away, and most importantly, a patisserie just down the street. It was about 10 Euros by taxi from the Santa Maria Novella Station -- possible to walk if your luggage is light.
Overall I can't imagine a better place to stay in Firenze.