The Teatro alla Scala is one of the most important Opera Houses in the world, having been performing renowned operas since 1778. At La Scala you can see a ballet or an opera and in my opinion is a must do experience. Prices for a show are around 30/40€ for a nice spot.

There's also the possibility to just visit the theatre, which is a nice thing to do in my opinion. Tickets for this are €12 and you get to see the theatre from many perspectives.