Pisa is about an hour away from Florence, between which there's Lucca - birthplace of Leonardo DV.
Then there's San Gimignano's fabulous duomo & Siena's traquility & il Campo. Things to do include:
1. Wine tasting in the Chianti region (no better place in italy)
2. Horseback riding
3. Water rafting.
Heck drive down Cinque Terre toward La Spezia if you're feeling adventurous. Best coastal views in Italy. Spectacular. Magnifico!
Florence itself is a town you can cover in 1 or 2 days, depending on amount of time spent in museums and churches. Must vistis include the accademia (mike's david), the duomo, santa croce, and of course the Ulffizi.