Tuscan Winery Visit Recommendation

The family and I are headed to Italy in mid-June and will be in Florence for a few days. I am planning to do a day trip to Tuscany, visit a town or two (thinking about going back to Sam Gimignano). I expect to have the time to visit one, possibly two winery’s, and was hoping for some recommendations? In a perfect world, it would be a more traditional producer, with the potential to try an older bottle or two. I understand Castello Volpaia is decent, especially given the scale for the kids. But for this, it would be great to see someone a bit off the beaten path. Thanks much in advance,