Nathan's of Coney Island and Sabrett/Marathon (which are served at most of the other places Motosport mentioned) are both top notch hot dogs with a nice snap and flavor. I take mine with mustard and kraut. Just perfect.
I personally prefer all-beef natural casing dogs (like Nathan's/Sabrett) that typify the New York hot dog over other varities such as the German-style hotdog.
Search for hotdoglover's posts on this Board for more insights on the NYC area hot dog scene.
My all time favorite is a Nathan's Hot Dog in Coney Island. Maybe it's the sea air but it just tastes great.
I am sure there are gourmet hot dog places but otherwise we like: Katz's, Sarges, 2nd Av Deli, Papaya King and many of the street cart guys have good NYC hot dogs.
179 E 86th St, New York, NY 10028