the truth as I know it
try here: http://www.floroom.com/
dunno about staying, but you haven't been to florence until you've eaten vivoli ice cream.it is located @Via Isola delle Stinche
When my family went to Florence we actually stayed in a converted nunnery in the hills outside of town. Since we didn't rent a car it depended a bit on us using public transportation, but I think it was totally worth it.http://www.fattoriadimaiano.com/en/
if you don't have budget problems, try this www.jkplace.com I think you'd love it (and the location is numero uno).ValeriaPS I've been living in Florence 6 years, in the city centre, as a reference!!!!PS2: if you have time and you like museums, try to book the visit to the Corridoio Vasariano (it's the corridor on the Ponte Vecchio which was connecting the Uffizi with Pitti Palace), now a portrait gallery but, despite the artworks, amazing experience
I welcome any comment, so happy to hear from you.