Based on your criteria, I would to the following: Rome, Siena, Florence, Lucca. You don’t need a car, the food in these regions is incredible - Lucca and Siena are very family friendly yet less touristic. A beach option is Giglio Island, which is close by
@wwarren probably has some good suggestions too, since he was also there this year.
Thanks! We haven’t thought about Lucca and Siena yet so we’ll look into them 🙏