Try the New York Archery Club: http://www.meetup.com/nycarcheryclub/ Per their site: "At this time there are 3 archery lane locations in the NYC area. Two are located in Queens, and one is located on Long Island. read more
The very best place to practice is with an archery club, in the facilities / on the site used by the club for this purpose. You can also practice on private land if permitted by the landowner (eg in your own garden). read more
Brooklyn/Chinatown New York City Archery and Axe/Knife Throwing Range - beginner through expert. JOAD and Summer Camp programs available. read more
The best place to practice is at a proper archery club. Failing that you need to ensure that there is no way you can cause damage to another person. Even with a fairly lightweight recurve bow a missed arrow can deflect and overshot the target by 50 m or more. A compound bow can carry over 100m. read more