I think dress depends on the show and the crowd. Generally you'll get a mix leaning toward suits, nice outfits, as most people come from work. Nicer, more 'adult' show or a special show, most people will dress nicely, even if it's jeans, people wear nicer, tailored fit, dark jeans with a shirt and jacket or a nice blouse. If it's, frankly, a tourist draw, you'll get the jeans and sneakers thing more. Upshot is no one will toss you out based on clothing.
I've seen gowns and tuxes a plenty but it's mostly at the ballet or opera (where there will also be people in general nice wear and the occasional scruffster) and/or galas or opening nights on B'way and more 'special' shows. But the ballet and opera people dress better in general all the time.
Interestingly (to me, heh) at the ballet or opera though, most every kid is dressed up (tiny suit, fancy dress, tights, mary janes), even if they go all the time, it's very cute.