This is such a great question with a lot of great answers. At risk of beating a dead horse, I'll add my experience. Typically, when I take my wife to a show we like to dress up. Of course since we don't live in NYC and given the cost of face-value show tickets, it's usually a special night out so we're going to be more dressed up anyway. That said, I've gone to shows in a full jacket, tie and slacks outfit and felt totally over dressed compared to most. Seems a (for lack of a better term) business casual is more the norm (khakis and a polo or button down on guys, nice pants or a skirt and simple blouse on the women). There are also plenty of folks that show up in jeans and t-shirts and as noted the occasional group in clothes that are even more casual (workout or running gear for instance). I may be more old school than my age suggests, but I just feel the audience shows a certain level of respect and appreciation for the show, it's cast, it's director, etc. through the way you dress.
That said, as I've posted in another thread, my wife and I are going to Kinky Boots on our anniversary and are both planning to wear a pair of red patent leather thigh high boots so not sure what that tells you :)