Duomo inside/outside (the only church in Florence with a free entrance), Battistero just outside to visit its famous bronze gates, Accademia to see the original David by Michelangelo, Santa Croce convent where Michelangelo, Galileo and other Italian glories are buried, stop for a light lunch in a local trattoria if requested (not included)
Uffizi painting gallery, Signoria square and Old Bridge area

This is just a suggested itinerary, as a private tour we can customize the itinerary at your pleasure.