The Heights or Jersey City Heights is a neighborhood in Jersey City, New Jersey, located atop the New Jersey Palisades, along the west side of the Hudson River. It is bound by Paterson Plank Road on the north, Highway 139 on the south, Hoboken on the east, and the Hackensack River on the west. and Penhorn Creek on the west. Its postal area ZIP Codes are …The Heights or Jersey City Heights is a neighborhood in Jersey City, New Jersey, located atop the New Jersey Palisades, along the west side of the Hudson River. It is bound by Paterson Plank Road on the north, Highway 139 on the south, Hoboken on the east, and the Hackensack River on the west. and Penhorn Creek on the west. Its postal area ZIP Codes are 07307, and portions of 07306.