While you're in the city, go see something off-broadway or even off-off-broadway! The tickets are very cheap, and you're supporting the arts, all while seeing what is (usually) a pretty good show! I just saw a show last week at the Flea in Tribeca and it was fabulous! The ceiling couldn't have been more than 12', but the lighting design was well done and the show was excellent.
To answer your question, however, Wicked is a great one, for lighting as well as everything else. I just saw American Idiot, and while I really didn't like the actual show, it was an AMAZING integration of lighting, video, and projection. If you're at all interested in the future of projection and video in live entertainment, definitely see that show. I didnt' see Spider Man, but I wish I had - even if it is a bad show, it does represent a huge leap of technology for live
theatre, and it would be a great one to see. Also, if you're bored during the day, go walk around the
theatre district to see what's going on. There are a number of shows loading in right now, and you can often catch stagehands out on their
smoke breaks who may be willing to talk to you, and might even be willing to let you come in to look around if you're really lucky. I have a good friend in Local 1 who I met just because I noticed the
logo on his shirt when walking by and struck up a conversation.