ztl

You can find out lots about driving in Italy by Googling, you guessed it, driving in Italy.

In the meantime, this extensive article about that, complete with links to details, can get you started: http://www.reidsitaly.com/planning/get_around/car_driving_tips.html.

And I liked this blog: http://italyexplained.com/driving-road-signs-italy/. There are links to 2 other major relevant posts and links to more info in all three, including the extensive Wikipedia sign list.

By the way, driving through a ZTL isn't the only way you can get tickets in Italy. Reading the info in these links should help you to avoid them.

More towns are adding ZTLs all the time. Some have "open" hours, usually in the evenings, sometimes on weekends. I would count on most places with a tourism infrastructure having them.

You can usually find parking outside the historic center.

I can't answer the full question without googling. But this summer I drove in Todi, Spello, Amelia, San Gemini, Bevagna, Orvieto and Deruta. All had ZTL zones except possibly Deruta (I didn't go into the historic centre, as the ceramic place I visited was outside it.) But all had good parking quite near the centres, and it was much easier to leave the car and walk in. By the way, an Umbrian native explained parking rules to me this way: white lines = free parking; blue lines = pay parking; yellow lines = don't even think about it. Yellow is for residents only or otherwise restricted.

Apart from ZTL rules, entering in central zones of ancient towns, usually mazes of one-way narrow streets is never a clever move. The thing to do is looking for collective parking areas just outside the center and leaving the car there.

Another clever thing to do is being on the look for forbidden access signs - round and white signs with a red border - and pass them only if you are utterly convinced that you have throughly understood possible explanations posted under the signs (explanations in abbreviated legal Italian that sometimes are difficult to understand on the spot even to natives).

The colors of stripes are not necessarily what Nelly posted.

Blue: Metered Pay Parking
Yellow: Restricted (Handicapped, Police, Emergency vehicles, etc.)
White: Check the signs. It may mean free, or it may mean residents only (like in Florence).

All the towns you mentioned, with the exception of Deruta, have ZTL. This is an example of a ZTL sign. The white circle with red border sign means "no motor vehicles allowed" (usually there are explanations below the sign, for exceptions and hours effective)
Look for this sign indicating a parking lot and leave your car there.

Thank you to all who replied. Last year, my husband and I drove around Tuscany without breaking any ZTL laws. I didn't know if the smaller (non touristy) towns also had the same laws. Thank you for reminding me of the colored marks for parking. My mind went foggy over the past year. Are there any other small towns, other than the ones I listed, that are worthwhile visiting?