Just come back from Florence. You should book the Uffizi Gallery and also the Galleria dell Academia (to see David). Both of these galleries have long lines that you can skip if you pre-book.
The Piazza d. Signoria has some great statues (I loved the Perseus holding the head of Medusa!) and also a David copy.
Other good places to visit are the markets around San Lorenzo (cheap Italian leather and wool), the Duomo, and Ponte Vecchio. For traditions sake, rub the boar statue's nose in Mercanto Nuovo (on Porta Rossa) and throw in a coin.