Our home base will be Orvieto while staying in Italy. We would like to travel to visit a few of the significant locations in Italy while staying in Orvieto where our son will be for the spring semester. There will be 5 of us traveling, our 3 children will be 18, 19, and 21.
Might as well take the one hour train ride to see Rome only if you have not been there.
Or we went to Siena from Orvieto last New Years Day. You just have to change trains in Chiusi-Chianciano.
You might want to consider Assisi and Perugia.
Todi is lively, bus schedules can be a little difficult, especially on weekends. Perhaps no bus on Sunday.
Yes--Sundays are very, very problematic for buses. Plan to use the train that day, stay in Orvieto, or rent a car.
You might stop in at the Orvieto tourist office, explain how long you'll be in town, and ask what their favorite day-trips would be. They should be familiar with what is easy vs. difficult by public transportation.