What should I see now that everything's closing?
I agree with Yankeefan007: highly recommend Time Stands Still! It's very accessible too, since you mentioned you've never seen a play on Broadway. I'll be in NYC a week later and have these on my schedule: Driving Miss Daisy (could be a nice option for you too), Angels In America (not sure about ticket availability though), Spider-Man (giving it a chance), Three Sisters at CSC, Gruesome Playground Injuries and American Idiot. I think you're going right during Billie Joe's "hiatus", right?