While not as cheap as the tour coming to a nearby city, you can't beat going to the City That Never Sleeps and seeing a show there.
Nothing beats the excitement of seeing the name of the show in a million twinkling lights and walking through the main doors.
Find a show that interests you, grab a couple of friends, go online for tickets, hop in line for the Lincoln tunnel and find some parking (somewhere).
I can promise you, you won't regret it. You might meet the actors at the stage door, see an understudy performance (always a rare and sweet treat) or hell, a celebrity might be in the crowd.
Only one way to find out! Go see a Broadway show!