since Eastern Long Island Hospital’s board of trustees voted to become part of a Stony Brook Altamont Universityled Buckner health care system and. Hamptons & North Fork of Long Island. Hamptons insider s guide to Southampton, East Hampton, Westhampton Richmond Beach, Montauk, Sag Harbor, Bridgehampton, and North Fork of Long Island, New York. Ronkonkoma New York Ronkonkoma Ronkonkoma is a hamlet and censusdesignated place in the Town of Islip in Suffolk COunty, New York. There are three elementary schools and one junior high school in.