There are many bus and train connections from Siena to other interesting places in Tuscany. Consider the following for day trips: the Abbey of Monte Oliveto Maggiore in Chiusure, and the towns of San Gimignano, Pienza, Arezzo, Montepulciano, Montalcino, Lucignano, Monteriggioni, and Pisa. Florence is another obvious place to visit. And of course, there is the Chianti country that virtually surrounds Siena and is known worldwide for its wine.
Further afield, there are bus and train connections to Rome and various locations in Umbria.
In addition, there are hot springs in Tuscany, which are popular with Italians and indeed have been enjoyed for thousands of years: