Overnight parking in Orvieto

You might want to try the Campo della Fiere lot above town. 5 E/24hrs.

http://www.inorvieto.it/en/plan/roads_car_parks_and_traffic.html

Is this the plan you are considering?

Drive to Orvieto from Florence or Siena (2+ hours), visit Civita di Bagnoregio, then Orvieto and sleep there.

Next day, drive from Orvieto to Assisi (also about 2 hours), visit there, then drive to Rome? (2.5+ hours).

It's feasible, but you'd want to get an early start. Driving estimates above are from Google maps, but search again at www.viamichelin.com for a more conservative and probably better estimate. Give yourself the flexibility to change your plan if you decide you want to stay longer in Orvieto. In the olden days, I did leave my car at the train station parking for a couple of nights.

Orvito has a central parling area nr the cathdral. It is pay until after hrs until 8 am. We parked there and left at 8am , a gd incentive to start early.mbut u are trying to squeeze in too much imo. Orvito and assissi wrrant. Day ea. Civita de b. Is a drive from orvito eventho u could see it in 2 hrs or so.
I would recommend choosing only 2 towns.

There are several parking lots in the city, but be careful of time restrictions - a fellow guest at a B&B had his rental car towed because he parked at Piazza della Repubblica the night before market day. Signs are posted around the piazze where and when you can park.