For New York City, you have to be a member of an NYPD - approved range/club. For Queens residents, go to the Woodhaven range across Jamaica Ave from Franklin K. Lane High School. For Manhattan, try West Side R&P.
You will neet to become a member of the range/club, and the clubwill prep you for your trip to the Puzzle Palace (One Police Plaza). Remember to bring your birth certificate and exact money orders. Be prepared to be issued a RESTRICTED - NOT FOR CARRY permit.
For Suffolk County towns of Huntington, Babylon, Islip, Smithtown and Brookhaven, go to the Suffolk PD HQ in Yaphank. For east enders, go to the Suffolk Sheriff's HQ in Riverhead.
Be prepared to accept a restricted carry license, to and from the range, or while hunting. Look into a key-in range such as Old Bethpage Rifle and Pistol club.
For upstate NY, call your county Sheriff - they may refer you to a separate office, in Delaware County that office is referred to as the Pistol Clerk.
In Delaware County, prepare for the shock of your life - a New York pistol licensing authority with respect for the Second Amendment (unrestricted carry)!