depends on what you want, here are my tops picks for good food, when I feel like crossing the bridge into the city:
Ramen - As others have stated, Ippudo can't be beat.
Bubble Tea - Saint's Alp Teahouse. The wife and I go here at least once a week...mmm, almond milk tea (no tapioca, please)
Yakitori - Yakitori Taisho. Really fun atmophere, but super limited on space.
Dim Sum - Jing Fong in Chinatown (for lunch on the weekends). You can't miss it, it's the one with the escalators on Elizabeth street (a few doors down from J&L trading for some import gaming goodness ;-)).
Beer Garden - Zum Schneider. You'll have to take a taxi to get here, but the beer selection is pretty good, and the German food is great!
Steak - I've been to several of the "big name" steak houses in NYC, and the best steak I've ever had in my life was at Bobby Flay's Bar Americain. I don't know what that guy did to that steak, but I would have gladly paid double for as much as I enjoyed it.
Pizza - John's Pizzeria in the theater district. Fantastic brick-over NY style pizza. Super-touristy, though, only because of where it's at.
Fish and Chips - A Salt and Battery. Somewhere on Greenwich St. Google it for the address...it's awesome.
That's about all I can think of. They may not be critically acclaimed, but I can nearly guarantee that you'll enjoy the food/experience at these places.