Both Aoki and Shimizu are good japanese choices for pre-theater Aoki is on West 48th Street and the other on West 51st Street. I go to either depending on location of theater. You will be able to keep within this budget without a problem unless you order lots of a la carte sushi or omakase.
Sushi of Gari just opened in the theater district, that could get expensive though. There's also Ruby Foo which is asian fusion and not bad or Blue Fin which is asian-ish! its more modern cuisine than asican but its good.