Where to drop rental car outside rome

Tiburtina Station. Most car rental companies have offices at or near Tiburtina. It's near the freeway exit.
Roma Termini is really not that difficult to reach either.
Some people might tell you to return at the airport. That is really easy, but from there it's a 50 euro taxi ride (45 min.).
Others might recommend Orvieto then take the train (75 min) from Orvieto to Rome. However I don't know where you are coming from and if Orvieto is not a stop on your itinerary on the way to Rome, going to Orvieto just to return your car wouldn't make any sense.

Roberto always has great information and advice. But for me, driving my rental car to the Rome airport and dropping it off there was well worth it, to avoid driving in Rome. The 30-minute high-speed train from the airport to Rome is 11 euros per person, and I believe a train departs every 30 minutes.

I agree that returning at the airport is very easy. However Tiburtina station is just as easy. Termini is also not that hard.
I don't know where you will be driving from, but check the drive on Google Maps to Tiburtina station.
The train ride is 14 euro per person, (it is not high speed train, it is a slow moving commuter train), the train ride is 32 minutes to Roma Termini station. In addition if your hotel is not walking distance from the Termini Station, you'll still need a taxi from the station to your hotel. If you have luggage I would not attempt taking a bus or the metro from the station to your hotel.
Since I presume you arrive to Rome with a car full of luggage and maybe a spouse, once you drop your rental car you probably need a taxi to the hotel. The fare from Tiburtina station to any hotel downtown is at most 15-20 euro and the travel time will be under 10-15 min. no matter where your hotel is, since Tiburtina is virtually in the city center. From the airport to your hotel is at least 40 minutes depending on traffic and the taxi fare is approx. 50 euro (plus potential charges for bags or tips, if any apply).

As Roberto suggested, if you have time for a visit to Orvieto, I would return the car there, see the town and then return to Rome via train (approx. 90 minutes). Orvieto is a lovely town and I really enjoyed seeing it. It's also a nice contrast to the hustle and bustle of Roma!!

If you're coming in from Tuscany / Umbria, then Orvieto really is the best choice. The car rental places are clustered near the train station. Orvieto is worth the stop to visit. Several trains take you straight to Rome.

Agree on Orvieto for car return from Tuscany road trip on the way to Rome. The train station was just across the street from the train station. We hoped on the train to Rome for end off our Italy adventure. We ran of time to visit Orvieto was our only regret.

The airport is pretty easy -- it works just like rental car returns in the U.S. Note that the road right before you get to the airport is a little scary if you aren't used to driving in a foreign country...it's a lot like your average interstate in the U.S. and people whiz by you pretty fast (but that's just Italian drivers for ya)! The train into the city is less than $15 per person and is safe, clean, reliable and convenient. Just another option to ponder.