I studied in Firenze for a semester, and it left quite an impression on me.
Tourists often leave without seeing the beauty that Firenze has to offer, but if you treat the city with respect you will gain much in return.
The Duomo is breathtaking—Santa Maria Del Fiore is the 4th largest cathedral in Europe. There are many other churches within Florence, ranging from Santa Croce that holds MichaelAngelo’s tomb, to Santa Maria Novella just a few feet from the central train station.
Florence’s food is spectacular (stay away from the center of the city/tourist spots)... The gelato is perfect. Firenze has so much to do, whether it be shopping, riding bikes, going out at night, listening to musicians in the streets, or meeting a friend in one of the many piazzas.
Most importantly, Florence houses some of the most important pieces of art from the Renaissance. Make sure to go to the Uffizi, Accademia (to see David, of course), Bargello, and the San Marco monestary.
I love Florence.