I went to NYC two summers ago with a group from my church, and one thing we did was go to Shakespeare in the Park. It was a FREE play in the park, it wasn't Broadway of course, but it did have several well-known actors/actresses (Zach Braff from Scrubs, Kristen Johnston, Christopher Lloyd, Julia Stiles, and several others). The play we saw was TWELFTH NIGHT. The only thing was that we had to go to the park in the morning and wait in line to get the tickets, but as I said, it was FREE, and it was worth it!
We really enjoyed that, not sure if it's something you'd be interested in, but I thought I'd share.