Umbria base without a car

Perugia is the most convenient for public transportation being the regional capital and regional transportation hub. It’s not a village, it’s a bustling city with a very large college student population. The historical city center is very pretty. I don’t think it’s an undesirable place, but you won’t have the small village feeling you would have in Spello or even Assisi. So it depends on your taste.
Spello has a station near the city center, which makes it very accessible. Assist’s station is down at Santa Maria delle Grazie so you need a bus to get to it. There are intercity buses however which stop closer to the city center. All other locations are nice to visit but not great hubs, but again it depends on what you want to see.
Cortona is nice, but you can also visit it easily on a day trip, especially if you stay in Perugia.

We had a fantastic meal on our own in Montefalco (l’Alchemista) during our stay on the RS Village Italy tour this May, but other than the restaurant and a lovely view of the surrounding landscape, there’s nothing to see and do there. I’d recommend you focus on other places.
We loved spending time In Orvieto. I also thought Civita was magical. We went at about 5:00 pm and it was not at all crowded. I suspect the same would true very early in the morning. I wish we’d had longer to explore there — definitely worth a couple of hours.
I would definitely look into day tours to wineries and other places outside of Orvieto.

I understand that Perugia has more public transportation opportunities, but I've also heard that it's not all that desirable. Thoughts on any of this?

We thought Perugia was great! Up on the plateau of the hilltown it is larger than many others such as Cortona so there are plenty of restaurants, hotels, and shops and we ate well there. Easy access to the top from the train station with the minimetro. Also car rental next to the train station although that won't be of interest to you. The TI folks were very helpful. I've never heard anyone say anything bad about Perugia before.

We researched for several days in Umbria, but COVID killed the trip.

Key places to visit are Perugia, Assisi, Spello, Spoleto, Gubbio, Orvieto and Terni.

I had booked staying in Perugia and using it as a base to train or bus to the other cities. We planned to visit Orvieto on our way back to Rome.

You can do Umbria without a car, but need to research your rail or bus connections.

We do have booked a Road Scholar tour for late April, early May, next year. The tour is called The Hidden Medieval Villages of Tuscany and Umbria. It starts in Siena, where Siena is the base city for visiting smaller towns in Tuscany, then moves to Spoleto which is the base for most of Umbria.
https://www.roadscholar.org/find-an-adventure/22977/The-Hidden-Medieval-Villages-of-Tuscany-and-Umbria

These responses are super helpful. Thank you so much.
Teri

Hi Teri,
We based in Bevagna nine years ago (the real estate agent gal who arranged our square-side rental there just emailed us yet again yesterday).
I'd also add Trevi to your list. Norcia seems to be back on its feet after the earthquake. And I'm forever trotting out poor Castelluccio. It can't be a base anymore (same quake) but as a daytrip, it would be special. Especially if one were to visit the latter for sunrise, when sometimes there is a thermal inversion that fills the entire valley with milky fog.
Terni? I would not select it over other choices on your list, unless you were catching a train.
Tante belle cose.
I am done. The end

I based in lovely Spello for a few nights and found it a great location for day trips to other towns in eastern Umbria. Do be sure to visit Spoleto.

Thank you very much, everyone!
Teri

I traveled in Umbria without a car about 15 years ago. It was in July, which would probably be too hot now. I was really glad I spent a night in Orvieto because it was so much cooler and less crowded in the morning and evening. I used Perugia as a base for several days and that worked well for both bus and train day trips, and I liked Perugia. I especially liked Gubbio for a day trip. I stayed one night in Cortona and wished I was staying a second night.