Hello tdrussburton, and welcome to the forum. That is quite a kick-off first post.
I spent a month in Lucca last year September into October and it meets some of your criteria. The historic center is inside the walls and is well defined and preserved feeling that way. But that also means it's not much of a sunrise/set vista town but feels more perpetual inside of the walls is that makes any sense. It certainly has many local shops, bakeries and places where only Italian is spoken and the aqueduct built by Napoleon's sister stills brings water to the town faucets and the old people (and us) went every couple of days to fill up their bottles for drinking and coffee. But the streets swell with tourists during the day and you hear a fair amount of English and German in the street. This also means the town has higher tourist priced rentals but also a concentration of a surprising number of good restaurants. These things probably fade in November but as I'm sure you know the other problem with tourist driven places is "the season" and how many things shutter when the season is over.
If you want the all Italian town in this area there is Pistoia which is larger than Lucca but on the same train line to Florence as Lucca and Prato (another town) which is not touristed.
The size of the town you are thinking of makes a big difference - it sounds like you want a very small town connected to a larger town by train. If you want really small you might look into Bagni di Lucca which is collection of small towns outlying Lucca and some are connected by train.
Given the weather closer to the Alps you might think further south headed into November weather.
Siena is beautiful with one of the all time great piazzas but way too touristy if you're looking to escape that.
Arezzo has much less tourist interest and great piazza and is blend of modern Italy on the flat near the train station that gets ancient as you head up the (steep at the end) hill. It is well connected to Florence, Cortona, Perugia, and Lago Trasimeno by train and Siena by bus. If you are there deeper into November these Tuscan towns (especially Arezzo) really lean into the Xmas festas and decorations.
Orvieto is very small but relative close to both Rome and Florence by train.
Two cities I really want to visit but haven't that might also work for you:
Ferrara - historical, 30 minutes to Bologna by train
Ascoli Piceno - more remote than other places 40 minutes to the Adriatic coast
My completely off-piste suggestion would be Venice which you can't beat for beauty and uniqueness. I know it is now largely a tourist attraction but speaking to our host last time he talked about how slow it is in November. Maybe a small place out of the way could give you the kind of experience you're looking for. November weather is a concern there and is also the greatest chance for high water if that is a plus or a minus.
The problem with "anywhere" is that there are too many choices.
Hope that helps some,
=Tod