Will be visiting both Sienna and Cortona Any info on Parking lots will be helpful.
For Siena, recommend the fortezza stadio lot or the parking by the train station.
https://www.discovertuscany.com/siena/tourist-info/parking-lots-in-siena.html
Having been to both cities with a car, I can tell you that parking, especially for free, is a challenge.
In Sienna, we parked near the escalator up to the town on the street. It takes patience and a bit of luck, but we have been successful both times.
In Cortona, we found free parking, but I cannot remember the location and it may not be there any more.
Good luck and be patience.
The underground parking lot in front of the train station in Siena costs 2 Euros per day - probably the best deal in Tuscany. We used it during a 5 day stay in the city a few years ago (pre-Covid) and never had any issues with finding a spot. It's located just off the SR2 making it a simple matter to get out of town and is well clear of the ZTL's.
Cortona had a couple of free lots but they fill up fast. One is by the escalator and stairs that go up to the town.
http://www.livingcortona.com/where-to-park-in-cortona/