We've been to Italy ten times or so as a family and only twice did we not have a car. We did Tuscany by train (Florence, San Gimignano, Lucca, Pisa), which was fun, culturally immersive, and affordable, but it meant exploring just one place per day. You're at the mercy of the schedules, but we did have a great time and little kids love trains.

The other time was an intentionally in-depth four days around Trapani, in Northwest Sicily. A blast, but we didn't venture far, except by boat.