Traditional broadway musical: Wicked, Finding Neverland, and the other big name shows you probably think of when you hear broadway

Dance: An American in Paris. The ballet is absolutely incredible.

Straight play: The Curious Incident of the Dog in the Nightie


I recommend the last one. I love Broadway musicals, but last time I went to NY, that was my favorite of the four shows I watched, even though it was a straight play. I would suggest watching that and one big-production type musical.