Quaint towns by rail from Rome

If it is a hotel, often you can check in and they will hold your luggage until you return and your room is ready.

Quaint is not a well-defined term, but one common answer from Rome is Orvieto. It's a rich destination. There are two major attractions in closer Tivoli, but the town itself is not quaint. Viterbo has some charm and is closer than Orvieto.

Which airport are you flying into from Spain? Fiumicino or Ciampino?
Honestly, I wouldn't want to be too far away from Rome Fiumicino the night before a transatlantic flight, assuming that's your airport of departure, and you're flying to the U.S. or Canada. What time is your flight home?

Don't forget about your need for a COVID test within 1 day of departure to re-enter the U.S. either proctored self test or administered by a pharmacy or other official testing site.

At Fiumicino, although I'd get it done BEFORE the same day as your flight:
https://www.adr.it/web/aeroporti-di-roma-en/test-areas-at-the-airport?p_p_id=it_txt_adr_cookiepolicy_web_portlet_AdrCookiePolicyBannerPortlet&p_p_lifecycle=0&p_p_state=normal&p_p_mode=view

What time is your flight to US?
If before noon I’d want to be in Rome the night before

Consider checking in to airport hotel, drop your bags and go visit Ostia Antica and/ or the beach there for the day
You’ll need to get COVID test that day as well

We were just there and stopped at Orvieto (we had a car and it was about a 1 hour drive from Rome). Orvieto is a hill town - here's Rick's article about it: https://www.ricksteves.com/watch-read-listen/read/articles/orvieto-what-an-italian-hill-town-should-be. It would be a good day trip for you.
We testing for COVID in Rome. I wouldn't wait to do it at the airport.
We flew out of Rome FCO to come home -- booked a cab to take us to the airport and it's a flat 50 Euro charge from Trastevere.

Thank you everyone. Our flight leaves at 10:00 am from FCO.

Welp
In that case you need to be there at 7 am
Your options are limited

Stay in Rome or at airport
You could probably day trip to Orvieto but still have to transit thru Roma Termini or Tiburtina

Landing at 9:30 means you might get somewhere by noon
Still need that COVID test

If you’ve never been to Orvieto it might be worth the extra train travel time to get there. The Duomo is spectacular and the town itself is charming. However, it is at least 2 hours each way and, realistically, based on current train schedules, landing at 9:30 probably means catching a train around noon which would get you in to Orvieto around 2pm. Using a random date in June, it looks like there is a train departing Orvieto around 7:30 pm, changing at Roma Tiburtina with a connection time of 28 minutes and getting to the airport around 10:30 pm. The only way that I see this working is if you stay at an airport hotel, most likely the Hilton. We stayed at the Best Western Rome Airport the night before our 10:00 am flight back to the US and while that worked out OK, owing to traffic and the shuttle schedule, it took quite a while to get from the airport to the hotel. (We had taken the train in from Orvieto.) So if you wanted to drop your bags before catching the train, that hotel might be cutting it close. Getting in to Orvieto at or after 2 pm would mean many restaurants would be nearing the end of lunchtime hours and not opening again to around 7. You could have your return Covid test done in Orvieto at the Farmacia del Moro right in the center of things. Very efficient — I’ve tested there twice. They give you a paper print-out of the results; cost is 20 euros.
All that being said the night we stayed at the Best Western we walked in to town for a last gelato fix, and while from that limited exposure, although it did not appear to be quaint, it did look like it could be interesting and a lot less effort than 4+ hours on trains before a long flight home.