It is a MUST ! If you go to New York, you must go to see a show on Broadway. I have gone 2 times in New York. The first time I saw CHICAGO. It's a musical that is always on Broadway, because it is very popular. I bought the tickets the same day and it was cheap and good location (of course not the best seats in the house, but good for the price). The actors are really good, and the songs too.
During my second time in New York, I saw The Lion King. Many people recommend to me that I must see it. It is an expensive show (US$100 if you buy tickets in advance but with good location) but worth it as it is a really really good show. I don't wanna say too much, because it is better to see whats happens in the moment. I just will say it is full of suprises. The actors are amazing, and the scenery extraordinary.