Do any of those towns have ZTL (zones of traffic limitation)? If they do, it seems very difficult to NOT drive in them, and the fines are high.
We spent a wonderful 10 days in Chianti, including day trips to towns southeast of Siena. We had absolutely no problems recognizing and avoiding ZTL zones including in Siena. We found ZTLs, especially in smaller towns to be well marked. We also assumed anywhere within the walls of a hill town or other village, such as Radda, San Gimignano and Volterra to be ZTLs.
We came home with no speeding tickets by strictly observing the speed limits and no ZTL fines because we could recognize the signs prominently posted. For extra assurance, you can go to websites with maps of ZTLs for numerous Italian towns and cities. We also opted out of driving in Rome and Florence, where dealing with traffic even outside ZTLs can be challenging.