Hell's Kitchen.

Hell's Kitchen is a neighborhood on the west side of Manhattan, roughly the area from West 34th up to West 59th Street, and from 8th Avenue over to the Hudson River. A good overview of the neighborhood is available on Wikipedia here.

Hell's Kitchen is sometimes called “Clinton," especially the part north of 42nd Street. Hell's Kitchen below 42nd Street is sometimes called "Hell's Kitchen South." That's where the flea market is located.

In Hell's Kitchen South you can still find small mom-and-pop businesses, including specialty food stores. The area near the flea market is relatively free of tall buildings, allowing for a surprising and sweeping view of midtown Manhattan, including The Empire State Building, The New Yorker Hotel, and the recently-completed New York Times Building.