I was just there and saw a bunch of shows and agree that people wear anything and everything but it's nice to make an effort. I was there in February when it was cold, and I wore skinny jeans, boots, silk blouses, and leather jacket and/or fur vest. (You can see photos on my YLF blog.) For July I would wear pretty summer dresses or capris and pretty silk tops, and great shoes.
And whatever you do, pay whatever it costs to the scalpers to see "Book of Mormon." Best. show. ever. No kidding. I got my tix from Stub Hub and paid a fortune and it was worth every penny!