The Museum of the opera di Santa Maria del Fiore:
The Medici Chapel:
and the Bargello.
I took one day to see the Tuscan countryside, here's a quick sketch:
Also, I recommend highly the hotel I stayed at, the Soggiorno Michelangelo Hotel. It is just north of the Accademia. I was welcomed by Oscar, who runs the establishment, and the accommodations couldn't have been better, or more quiet.