How I wish you had longer than 6 hours...oh well!
My recommendations:
(1) View Duomo from exterior
(2) Visit the Medici Chapels where you see stunning Michaelangelo sculptures draped on the tombs.
(3) Purchase leather gloves for yourself and friends at market near Medici Chapels.
(4) Have lunch at ZaZa's near the chapels and have their fagioli soup.
(5) Visit Santa Croce church
(6) Eat gelato at every possible opportunity.
(7) Enjoy a cup of coffee or hot cocoa outside at the Revoire and take in the people watching in Piazza Della Signoria
(8) Window shop as you cross the Ponte Vecchio but I don't think you have time to explore much of the area across the river.
(9) Statue of David is hard to pass up and the Accademia is so small that you could certainly include this in your visit.