There are dozens of possibilities. You might also consider some of the lovely towns in Umbria. You could even visit some towns in Le Marche, one of Italy's most beautiful and overlooked regions.
In Tuscany, Montepulciano, Pienza, Arezzo, and Sansepolcro are not far from Cortona. Arezzo is really a small city, rather than a small town, but you can see Piero della Francesca's great fresoc cycle in the church of San Francesco. There are other works by this great artist in Sansepolcro, which is a lovely Tuscan town that's off the tourist radar screen.
In Umbria, Todi, Assisi, Spoleto, Spello, and Gubbio are within easy driving distance. All are different and all are beautiful. You might be able to visit Assisi and Spello on the same day. Assisi has a lot to see, especially if you're a devotée of Saint Francis, or if you are an art lover, but Spello, a little jewel, can be seen in an hour or two.
In Le Marche, you could visit Urbino, a lovely Renaissance town on a hill in Le Marche, with one of Italy's most beautiful ducal palaces.It's worth driving up to the park above the town, to get a spectacular view of the palace. Camerino is another lovely Renaissance town in Le Marche, that gets hardly any tourists except Italians. Both are about a two-hour drive from Cortona, but with lovely scenery along the way.
Edited: 4:47 pm, January 18, 2013