You will see all manners of dress these days at the theater. Personally, I always look nice - business casual or dressed for a night out (cute top, dark jeans, nice shoes). Not suit and cocktail dress though.
Dining - there are a bunch of restaurants in the Time Warner Center and many are well-regarded, but I personally have not been to them.
Agreed that you will see all sorts of attire nowadays at the theater. I like to go dressed up where I can go out afterwards - sweater dress, skirt and top. I will do dark jeans and cute tops with nice heels and accessories as well.