Milano for the upcoming holidays

Hey everybody,
I'm coming to Milano in a week and will stay for two.
I'm happy to go there and, though it's gonna be my first time in Milano, absolutely sure I'll be able to find the main sightseeings from the tour-guide. Still, I'd love to visit some non-touristic places in and around wonderful Milano. Please, let me know what are your favourite places to spend your spare time. If there are any places with high-sight view, that'll be great!
Besides, I'll be there for both X-Mas and NY, so if there is a good advice and tips about how to spend these romantic holidays, I'll be grateful.
Thanks,
Svetlana.