Whenever my husband and I go to NY we always do Broadway... What we learnt (on our later trips) is there is a ticket booth in time square (underneath a big out of place set of stairs..I believe under the bleachers) you can buy tickets to the discounted show of the evening for super inexpensive.
We bought $280 tickets to see Wicked and as we headed back to Times Square we saw the booth and sure enough they were selling $60 tickets to shows that Hugh Jackman was starring in and also shows that Joseph Gordon Levitt was starring in!
There are a lot of fun things to do in NY, i'm sure you will have a blast. When we go we eat, drink, we've cruised Irish district (hubby's irish), cruised Chinatown, gone to Ground Zero, and always see a broadway show!