Orvieto is beautiful. The ticket for the funivia (across from the train station) is also valid for the minibus that takes you to Piazza Duomo. There are two bus routes: the longer one takes you through the winding streets, really a fun ride, only takes about five minutes or so longer than the direct bus.
See the Cathedral, and go to the museum across the street for a view of the mosaics on the cathedral facade from the upper floors of the museum - they look close enough to touch.
Saint Patrick's well and the ruins of a castle are on either side of the funivia.
If you are there on a Thursday or Saturday morning, there's a market in Piazza del Popolo. The TI office in Piazza del Duomo is very helpful.
If you are not spending the night in Roma after you visit Orvieto, leave your luggage at the Roma Termini station, the train station in Orvieto doesn't keep baggage (although I've heard there is somewhere near the station that does), you will probably have to connect in Roma to go to Sorrento.