This cathedral is incredibly beautiful. It was built in the 1300s and it's the fifth largest church in the world and the largest in Italy, which is pretty amazing. The gothic architecture and stained glass windows are stunning.
We bought a combo ticket that allowed us to visit the museum and to climb to the top (via stairs). It's a little extra to climb to the top using an elevator.
The museum ticket gave us access to the space under the church with pretty cool tombs and the old foundation.
We climbed the stairs to the top, which was kind of strenuous, but also made the view from the roof really rewarding.
We didn't actually go into the Castello - mostly because there were hordes of school children everywhere and we weren't in the mood to deal with that - but there's an amazing art gallery inside so if you're into that or maybe if it's a rainy day, it's worth a visit. If you're not into that, then just sit by the fountain and enjoy.
We were in Milan about a week before the World Expo was starting and there were a few displays already set up.