Interesting villages around Orvieto

Todi . Less than 1 hour away. Classic Umbrian hill town, smaller than Orvieto and wonderfully scenic. Montefalco and Bevagna
are about 1 hour from Todi. A little further afield but definitely doable in Southern Tuscany are Sovana, Sorano , and Pitigliano.

Brad

Also Civita & Bagnoregio.
[Edit: Yes, I meant Civita di Bagnoregio. Thanks Zoe.]

I think Kent means Civita di Bagnoregio. Definitely visit Todi, it's beautiful. You park in a public lot and take the little bus into the centro storico.

Spello is also very nice (Google maps says 1:18 by car from Orvieto, for what that's worth).

Well, if Spello is 1 hour, 18 min away, then Assisi is about the same. Certainly a small town, not really a village, but wonderful and with many sites to see, especially the Basilica of St. Francis, plus good restaurants and interesting shops. Certainly merits a good full day or more.

I also really enjoyed Gubbio. Note that the most central parking lot is expensive, but others nearby are free; you can run into the Tourist Office to get a map. Since that's about a 2-hour drive, you may prefer to take a new hotel, instead of daytripping; I liked www.grottadellangelo.it. Under the assumption that you will return to Italy, I would give some priority to the destinations that are really facilitated by having a car on this trip.

I enjoyed Bolsena on the lake just to the west of Orvieto

Spello, Montefalco, and Bevagna could be seen together in one day. Also, Pitigliano, Sorano, and Sovana could be grouped together for another day trip. Of the two groupings, I think the latter is a little more interesting.

Bolsena is a great idea, I was there for the first time last year. Castle, volcanic crater lake, and the best gelato in the world (handmade, six or so flavors change daily, little shop on via Santa Cristina; they close for an afternoon break).