If you have only one day, make sure you do the following (starting from the train station):

1.  Go to San Lorenzo (Nice Church to see).

2.  Then Accademia (Where David is, worthwhile, make sure to check this!)  You must prebook to avoid waiting in huge lines.

3.  Go to Baptistry and Duomo @ Piazza San Giovanni (very impressive church and dome), Take time to climb to the top of the Duomo the view of Florence is breathtaking! 

4.  Walk then to Piazza Republica (nice area to have lunch).

5.  Walk over to Palazzo Vecchio (make sure you go into the castle, the first of Medici, splendid).

6.  Galleria degli Uffizi (the best art gallery, takes a while though) in the middle are some nice statues to see of Galileo, Leonardo da Vinchi and others....don't miss it, but you must pre-book to avoid long lines.

7.  Cross Ponte Vecchio (oldest bridge in town, check out the jewelry).

8.  Head down on Guiciardini to Plazzo Dei Pitti (where the second of Medici, even better than the first one) and Bobli Garden!

9.  If you have time, hit up Michaelangeo (awesome view of the entire city!).

10. Santa Croce is a church which houses Michaelangelo and Galileo tombs...and a beautiful altar.

One should really try to spend more than one day in Florence...to experience Michaelangelo, Leonardo da Vinchi, Galileo and the Medici's.

This is a lot to do in one day, and you might want to skip Galleria, although many works of Michaelangelo are housed there.  The best restaurant is on San Antoni called Restaurant Nuti, with a pizzaria called Nuti across the street (same restaurant, just two places)...make sure you eat pizza and gelato...the best ever!   If you have only one day in Toscana, it is worthwhile to do all 9 quick (and not do 5,6, and 9) and go to see the Pisa Tower. There are trains departuring every 30 min and the trip takes 1h (and you can get there around 17h).