For a fantastic time and a chance to take in the local "color," consider an afternoon visit to with the Viola if they are playing during your stay.  Fiorentina, the "viola" due to their purple uniforms, play just 1 1/2 miles from the city center in the Artemio Franchi Stadium. The team plays in the Serie A, the top league in Italy.

The stadium is not large (by American football standards) and does have some covered seating.   Ticket prices vary and can be purchased at ticket offices located near the stadium.  It's possible to buy tickets in advance at the booth called Chiosco degli Sportivi off Piazza Repubblica (via degli Anselmi), but it's really unnecessary -- tickets are available at the box office for most games, except perhaps the biggest rivalries (e.g. Juventus).  Do not bother trying to buy tickets online.

To get to the stadium you can take the #17 bus from Piazza San Marco.

For those who have heard of violence in and around soccer venues, this particular team and stadium is less prone to such and you will find a very nice atmosphere present.   Just use common sense and you should have a great afternoon.

More info can be found in this article