When my children were little, we used to take the subway to Coney Island in Brooklyn, New York to eat at the original Nathan's. It was and still is a New York institution. We would stand around at the counter enjoying our hot dogs and delicious, thickly cut french fries. There were always long lines. Then we would walk over to the boardwalk to enjoy the fresh seabreeze and fireworks.
Nathan's has franchised itself out at many airports around the United States ... but you'd have to come out to Brooklyn for the quintessential New York experience.