Small town Italy

Which region?

What time of year?

Where will you be coming from, and where will you be going to afterward?

As others mentioned, we need more info about your plans. There's a wonderful book that was published in the 1980s titled Cento Citta https://www.amazon.com/Cento-Citta-Guide-Hundred-Cities/dp/0805007288

Obviously times have changed in 35 years, but the descriptions may whet your appetite for certain towns that you'd want to research further.

Sarzana, Liguria

If this is the first stop in Europe, I'd hope to make it a place that's not a terribly long slog from my arrival airport and also a place that doesn't turn the flight into a 20-hour marathon.

For a trip between May and September I'd probably want to avoid places in the south. Between November and March, at least, I'd avoid the lakes and the Dolomites.

Those limitations leave hundreds of options. It will probably be easier to find a charming but relatively non-touristy place outside Tuscany. Maybe Emilia-Romagna, Lombardy or the Piedmont?

I'm not sure I've been to a place as small or as devoid of tourists as I think you're hoping for. Maybe Tuscania, a walled town of about 8000 in northern Lazio, west of Viterbo.

Wikipedia entry for Tuscania
Community web portal: https://www.comune.tuscania.vt.it/

For Tuscany:
https://www.borghiditoscana.net/en/category/villages-en/
All regions:
https://borghipiubelliditalia.it/borghi/

Take a train from Rome to Chiusi then a bus to San Casiano dei Bagni.

Off season Viterbo has few tourists. The historical city center—within the wall—is charming and entirely walkable. Lots of places to visit and stay. Rome is two hours away by train.