I know I will get flamed for this suggestion, but (quietly) -- skip the
Uffizi. It will eat up an inordinate amount of your time. If you just
decide to see David at the Galleria dell'Accademia, it will take 30 minutes
(try to reserve tickets in advance.) Spend some time in the San Lorenzo
market before or after seeing the Medici Chapels, you should see the
Baptistery and the Duomo (in the same Pza. S. Giovanni), and then just walk
around the triangle from the Duomo, to the piazza S. Croce, to the Ponte
Vecchio. You can choose which municipal buildings, churches, and museums
you want to go into in this area, based on your interest and on your time.
The thrill that you get from Florence will be from walking these streets
just north of the Ponte Vecchio, and while perhaps taking lunch in the
piazza della Signoria.
Others on this list will give you equally valuable suggestions, and you
will just have to either make painful decisions, or walk very fast.
This is like performing triage.