Stuyvesant Townâ '' Peter Cooper Village is a large , private residential community on the East Side of the borough of Manhattan in New York City , and one of the most iconic and successful post-World War II private housing communities . Stuyvesant Townâ '' Peter Cooper Village is a large private residential development on the East Side of the borough of Manhattan in New York City , and one of the most iconic and successful post-World War II private housing communities .