I suggest you the Cathedral (Sanbta Maria Del Fiore and its Duomo), il Battistero, Piazza Del Duomo and Piazza San Giovanni, Piazza della Signoria, le Uffici (museum very interesting and absolutely great for its paintings, sculpures and environment!), all these sights are located in the nearly same area.
Don't miss Piazza and Palace Pitti, on the other side of the River, cross thus the Ponte Vecchio (interesting for jewelery).
Go also to FIESOLE, by bus. A very small city but offers you an incredible view on FLORENCE and its Arno river.

