if you are already there, the kids will love going to the top of the Duomo, which is one of the most impressive cathedrals anywhere in the world. You can also take them to the Galleria in the same piazza to spin on the bull's balls, which is a tradition with the Milanese. One of my favorite restaurants in Italy is in Milan - Il Paiolo with one of the best lobster linguinis anywhere on the boot.
While the kids may not be art lovers, The Last Supper is stunning. If there was a reason to go to Milan, it is to see the Last Supper. Probably my favorite piece of art anywhere. Da Vinci's work here is simply incredible.
Lake Como is just a short drive north of Milan, and is beautiful. I recommend Varenna. Bellagio is typically overrun, and Como is a bit industrial.
Unfortunately, the kids are too young for the great zip lines (such as the one in San Vigilio), but there are some great Alpine slides. If you like amusement parks, Gardaland is on the shores of Lake Garda. Sud Tirol is my favorite place in the Alps, hands down. Spend the night in Santa Magdalena in Val de Funes, and watch the sunset turn to a fiery alpenglow on this view:
And I promise you, that photo does not do it justice. Take the time while in Sud Tirol to visit Ortisei, a beautiful town and the source of lots of wonderful Germanic wood-carving. Some great hiking, biking and cable cars there as well.
Turin is a beautiful city with the Egyptian museum and the shroud of Turin. Turin feels much more French than Italian.
You can take the cable car to the top of Monte Bianco (Mont Blanc), for some of the best views anywhere in the Alps, and the drive from Milan through Valle d'Aosta is beautiful. After that, take the Mont Blanc tunnel through and stay in Chamonix, a lovely French mountain town.
You can actually visit Zermatt/Matterhorn from Milan easily as a day trip, which is good, because Switzerland will cost you a small fortune, the food is average, and the company typically leaves something to be desired. I've done the day trip from Milan six or seven times, and it's easy and a nice drive.
Keep in mind that once you are in Milan, you're only about a three-hour drive from Venice, and Verona and Padova (with Giotto's magnificent Scrovegni Chapel) are on the way. It's actually typically faster the take the A4 all the way to Venice than the A22 to Bolzano into Sud Tirol. In the summer, the A22 to the Brenner Pass into Austria can be a parking lot in places.
And I just realized that I left off one of the gems of the Sud Tirol - Lago de Brais.