My favorite restaurant in NYC:
http://www.patsys.com/ Broadway and 56th St.
Not a tourist attraction, family owned, a bit pricey but worth it. Over the years, just by chance when dining there we met Roger Daltry, Rosemary Clooney and several other celebs who go there to get away from the crowds and media. The walls are covered with signed photos of their famous patrons.
Ask to meet Sal, the chef - he's a real NY personality!