Take note that the Hertz rental at the Orvieto station is open on Saturday until 12:30 unless you pay for a late pickup....and then you may only pickup up to 2 hours later....for a fee.
As was noted, you must call Hertz to make your reservations.
You will find the Hertz just up the street (South and out of sight) to the left of the train station as you exit....refill the car right across the street when you return.
The restaurant next to the funicular serves a good workingman's lunch for a fair price...join the locals for a heaping Carbonara...
If you rent from there you can get to a great number of interesting places. Consider Tarquinia for the Etruscan necropoli...just a short distance beyond Viterbo...Viterbo is also interesting....and if you need to exchange cash the Main Post office there is about your only option in that region.
If you go to Civita, try to drive as close to the walking ramp as you can..there may be close parking...don't settle for the first spot you see. Pass the church of Bonaventure and look to the right.
In Bagnoregio there is a new gelato shop just up the hill on the right past the arch.....compare it to the others...
Good luck.