I'm going to the mediterranean for a few weeks in June also. In Italy, we're hitting Rome, Venice, Naples, Almalfi Coast, and Sicily but not Milan. Have you booked airline tix yet? The best prices I've found are $1600-$1400 roundtrip, which seems a little pricey to me. Despite that, I'm finding it's more difficult to get around Italy once I get there. Taxis are not the way to go (no pun intended) and I've been finding & booking private drivers. I saw Bob's link to the motorcyles and was tempted to look closer into renting one of those but after barely passing the BRC I swore I wouldn't get on a bike anytime soon.
In Milan there's lots of great shopping so long as you pay no mind to the current exchange rate
There's a wonderful opera house. Even if you're not a huge fan of opera, it would be pretty cool to go to an opera there. And if you'll be in Milan in early June, you may be able to catch the Festa del Naviglio - a huge street festival.
If you find any Italian language classes/tutors, please let me know. I used to speak fluent Italian many years ago and am looking for a refresher. The only classes I've found so far are in DC at Casa Italiana.