While Milan is not a super touristy city, the area surrounding the Milan Duomo and the Galleria Vittorino Emanuale II will make anyone think otherwise. This area is Milan tourist central and a great place to get pick pocketed, scammed, or just overcharged for food and drink. Enter, Liuni Panzerotti, a tiny, local restaurant jammed into the center of touristy Milan (just a block away from the Duomo). You should definitely plan to grab a snack here.
Milan is a really popular Italian airport for international flights, and unfortunately many people fly in or out of Milan without leaving any time to see the city itself. They travel in from Lake Como or Florence (on the fast train) the day of their flight. While this is convenient and allows time to see more bucket-list sites in Italy more touristy destinations, I think most tourists should spend at least 24 hours in Milan. That way, getting to/getting off your flight is not as stressful, and Milan is a pretty fabulous Italian city that is completely different from any other!