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Generally I'd recommend wandering around the downtown and looking at all the ridiculously expensive shops, go to the Galleria for sure. I liked the http://www.gam-milano.com/it/home/ a lot.
I had a bad experience at the Lancaster Hotel (bed bugs!).On Lago di Como take the slow boat if you have the time, it's just beautiful and relaxing to putter along between the villages.
Sorry, my info is dated (2010) and can't really say which hoods are desirable places to see and be seen in.
Have a good time!
Good one, just booked a couple of days in Nesso just around the corner. We'll stay in Milan for 2 nights before we go to Nesso, any ideas which neighbourhood to pick in Milan?
We usually look up the AllSaints store and find something closeby, but the Milan AllSaints is in a big mall rather than the trendy, up-and-coming, semi-gentrified neighbourhoods we're aiming for.