You don't say how long you have, and that makes a difference. Will you be traveling by car to Florence from Siena and then back south again to Orvieto? Although the distance is short, you have the Chianti region to explore north of Siena, and Monteriggioni, a turreted, walled town just outside of Siena to the north.

Near Monteriggioni, but often overlooked, is Abbazia Isola, a small town that was a pilgrimage stop in the middle ages. An even more impressive abbey, now in ruins (but walls still standing), and one of the most atmospheric spots in Tuscany, is San Galgano, a marvelous structure from the 13th century. You will also find the 12th century chapel where San Galgano himself is reputed to have plunged a sword into a stone when he gave up warfare. The sword and stone are still there to see.

San Galgano is south of Siena, as is the Abbey of Mount Oliveto Maggiore, a Benedictine monastery which is still functioning. There are wonderful frescoes by Signorelli adorning the passageways, and you can visit the on-site winery. The Torre restautrant outside the gates is an excellent place to stop for lunch. That's three abbeys, and all are within thirty or so kilometres, if not less, of Siena. There's lots more to see on route to Orvieto, with
Pienza, Montepulciano, and Montalcino all worth the better part of an afternoon, the latter especially if you like wine, since it is the epicenter of Brunello. There are some other small towns along the way to visit, and the countryside of the Val D'Orcia, which lies to west of the main road from Siena to Orvieto makes for lovely driving on uncrowded country roads. So all of this could be four of five days,