I think it's really hard to recommend just one "must-see" show unless we know more about what you really like and what you've seen already. Are you sure you can only afford to see one show? There's the discount ticket booth (TKTS) near Times Square; you can get same-day tickets there for nearly half-price (depending on the show and the seats.) There are also student rush tickets available for many shows, and even standing room at some.
That said, the ones that I think I would see if I were visiting NY would be Grey Gardens, Spring Awakening, Spamalot, Drowsy Chaperone and Company. But I'd definitely suggest that you read up on each show you're considering to see which ones seem most appealing. Hairspray and Jersey Boys are also a lot of fun!
Karen
Maggie-the-schnoodle