It looks like a really fancy city, everything looks beautiful, but a little bit cold. We couldn't find real party locations, just places to get together with people, but it's important to get out early, because they have happy hours, and after 23 and 24 everything starts to die, and prices get really expensive. As it is a big city, there is need to walk and travel a lot, there is not a geographical centre where to find everything. The main square is really beautiful, with the Duomo.
Insider Tip:To go out drinking, Porta Genova is a good location, you can get shots for 1 or 2 euros and drinks for 4 euros. But in that area there are also expensive bars. Go right when going out of the metro.
Don't miss visiting Luini, it is a backery with cheap traditional sweet and salty fast food. You will find it on a street on the left of the Duomo when looking at it. It is easily recognisable for the long queau there is always in the door.