Merritt,
Ron's link is excellent and should give you lots of possibilities.
I thought the Underground tour was interesting, as it covered a lot of the history of Orvieto including some more recent history.
St. Patrick's Well is also a very important part of the history, and it would probably be interesting to your children (as long as they're not claustrophobic!). The walk to the bottom and back could probably be done in 30-45 minutes if you're in a hurry. The double helix construction was an incredible achievement, considering when it was constructed.
The Duomo is definitely worth seeing, especially the ceiling frescoes at the end (to the right of the altar as I recall). The Frescoes tell a story, which I believe Rick details in the Italy book.
Of course, sampling some Orvieto Classico and some Gelato (not necessarily in that order) is also good. It's a fascinating town to just explore.
Happy travels!