Last year I went to Milan with my best friend. It was our first trip without parents. So much fun because we could do whatever we wanted and we all did it our way. We have a special way haha ;) 
Of course we strolled around in the shopping area. So so so nice! They have all the shops, and they are so gigantic. You need 2 hours for one shop. Take your time for shopping is the message Milan is screaming out, shop till you drop! 
Shopping was of course not the only thing we did, we visited the touristic stuff as well. We saw the Duomo,  the galleria Vittorio Emanuele and some museums but we did feel like locals haha actually we were just hoping we lived there.