Here are 4 choices for an easy day trip from Florence:

Siena:  It's easy to take a day trip from Florence to Siena.  A bus taking about 1.25 hours will do it.  Another way to go is to take the 1.5 hour train.  The advantage to the train is that it can be a little bit less hectic than the bus.  The Piazza del Campo in the center of Siena is one of the most famous piazzas in Italy and is a good place to enjoy a gelato.  The Duomo is spectacular as well as well as the frescoes at the Piccolomini library are well worth visiting.  Get the best view of the city and surrounding Tuscany area from the panorama viewpoint at the Duomo complex.  

San Gimignano:  Unfortunately, there is no train to San Gimignano from Florence.  There is a bus but you may be better off hiring a private car.  San Gimignano is a delightful medieval city perched upon a hilltop and probably has more charm than much larger Siena.  I would recommend combining a trip to San Gimignano with a trip to a winery like the Tenuta Vineyards.  Over the years, we have found Traveling Professor travelers prefer San Gimignano over Siena if they had to make a choice. 

Pisa:  Everyone wants to see the famous Leaning Tower and Basilica in Pisa.  Be warned, it is one of the most touristy places in all of Italy but it is worth the half day visit.  Get one of the may direct 40 minute trains from Florence to Pisa then take a taxi to the Field of Miracles to satisfy your urge for a day trip to Pisa.

Lucca:  The day trip from Florence to Lucca has long been one of The Traveling Professor's favorite trips.  It can actually be combined with a day trip to Pisa.  There are twice-hourly trains to and from Florence and regular trains between Pisa.  Lucca is one of the wealthiest cities in Italy, it is acknowledged to have some of the best food, and it is a perfectly preserved medieval city.  The ramparts circling the city are perfect for a leisurely bike ride.  The botanical gardens are peaceful and beautiful. Enjoy the view from Guinigi Tower and check out the home of Puccini, a master of opera.  There always seems to be a market, a concert, or some other activity going on in Lucca.