place to stay north of Rome for night before a flight to Athens and travel time/airport check in

Orvieto- Leonardo DV airport is 90 miles, around 1 1/2 hrs. You would need to drop the car, then be inside the airport at least 1 1/2 hrs for an inter European flight. So it would be doable if you left early enough.

Different travelers have different travel styles, some would do the airport hotel thing and others would be more, uhm, adventurous or more willing to roll the dice a bit with respect to their departure flight.

Staying in Orvieto or other place to the north, there's going to inevitably be some uncertainty regarding what traffic will be on the drive in. I've been told that getting some place in Italy sometimes takes longer than you think. What will traffic be like, will you get even a little bit lost on the drive in, will you find the airport car rental return on the first try--all of this with the clock ticking.
Easier to do here, but may not be so easy to do over there.

It's not ideal (there's no ideal solution to your situation and we've all faced it)--but what I've done when returning a car to FCO, after having been in Tuscany/Umbria, is to return the car in the later afternoon or early evening, the day before the flight; then taking a taxi or hotel shuttle to an airport hotel (reserved in advance, of course): a hotel that specifically tells you, by e-mail if needed, that it will facilitate your transportation back to the airport in the morning, either with a hotel shuttle (best) or by calling a taxi. Since you're flight departs at noon, airport hotel shuttle should be operating, so if you pick the right hotel, you should get a free ride to the airport. Usually taxis back to the airport are only necessary for earlier morning flights when the hotel shuttle is not operating.

The airport hotels are no worse or better than airport hotels anywhere else--you're just using it as a bed, but at least you're near the airport and don't have the uncertainties about trying to drive the morning of the flight.

Other travelers reporting in here have spent their last night in Rome (even if they've been up north and been in Rome previously, even on the same trip). That is, they return the car the evening before, then have to get into Rome, then back out in the morning. Seems like a lot of work, but you do get to spend your last night in Rome, maybe you treat yourself to a high end hotel and a great Italian meal?

Bracciano or Anguillara on lake Bracciano? Civita Castellana? Monterotondo?

If you stay in Orvieto don't forget there might be traffic on the GRA (Grand Ringlike Beltway)

Last fall we did what Kent suggested, returned rental car late afternoon the day before the flight. Stayed at Hilton Garden Inn at the airport but there is also a Hilton Hotel there. From the car return we had to take a shuttle that goes to the remote parking lots to get to the Hilton Garden Inn and the shuttle was not well identified. However one can walk to the Hilton Hotel from the car rental return. Hilton Garden Inn was very nice. Pricey food for dinner at the H G Inn but we had picked up food from a grocery in the afternoon to eat in our room. Coffee in the room. Pricey breakfast as well or one can find a nice cafeteria at the airport for breakfast. We had stayed near Orvieto a few days before our flight home but didn't want to take a chance on the morning drive and car rental return. Glad we stayed at the airport---less stress.

Kent's advice is very sound. Stick with it. Enjoy your wonderful vacation.

Orvieto is hard to miss, you can see it from miles away. I would happily stay there for a night if I didn't have an early flight out of FCO. Drop off the car in Orvieto, take the funk is up to the town, and have a nice stay in this beautiful place.