Our son (now 22yo) turned 12 when we were on a trip to the Dordogne area of France, and we did a number of the things mentioned here. He got a special pastry for breakfast, and we gave him the total choice of what to do that day. We did tell the waiter where we had dinner that it was our son's birthday, and they brought out a small cake (torte) as his dessert, with a sparkler, and the owner of the restaurant sang the French version of "Happy Birthday" to him. It was special!
What does your son like to do? There are tufa caves in (below) Orvieto; I've never been in them, but he might enjoy those. Depending on where in Tuscany you will be, if he likes castles or walks/hikes, there's a old ruined castle in the woods south of San Gimignano, called (appropriately enough) Castelvecchio.
Enjoy!