You can explore other towns in Tuscany by train quite easily. Siena is 1 1/2 hours away and perfect for a day trip. The cost is maybe three euros or so in each direction. Lucca is around one hour away by train, and a lovely old town still with its 16th century walls, medieval towers and old buildings.. Lucca is quieter than Florence or Siena, less crowded with tourists. Go on a Sunday morning when it is quiet and peaceful and you can appreciate the old world feel, then watch the town come alive as its residents come out to stroll the lanes. It is possible to make a half day trip to Arezzo to see the Piero della Francesca frescoes. Make a reservation online to enter the church after checking the train schedule. Be sure you buy a ticket from S.M. Novella train station in Florence (it has three stations). You can go by Eurostar in 1/2 hour, or by slower trains in one hour. Actually, if you use the Eurostar you can do day trips to Rome or Venice as well.

Another day trip would be to go to the outlets of designers just outside the city. There are good buys here if you are into designer clothing and accessories. The main outlet center is called The Mall. A coach tour of the outlets can be had through tour companies for around 25-29 Euros. Your hotel should have a brochure from one of them. 

Villas and Gardens. One of the lovliest gardens around is at Villa Gamberaia (10 Euro entrance).  The fiat 500 tours company take groups in vintage Fiat 500s to Villa Gamberaia (great gardens, very well known in the area). You can take a picnic up there for some stunning lunchtime views.  You could also get the bus up there, which is the cheapest way.  See the web for Villa Gamberaia.  It is close to town, but away from the crowds, (imagine about 40 mins on the bus with a bit of a walk at the end, it take 20 mins on the vintage Italian car trip, or a taxi would be about 20 mins too).  Ask in the hotel, or look on the web for details of the villa and garden history, and how best to get there for you.