http://www.nyc.gov/html/dep/html/wat...maps.html#maps

The DEP owns a bunch of land in the Hudson valley and the Catskills most of which is now open to hunting. Above is the link. You need a special access number and hunting tag, but it's all free and you could get it on-line. They even have a bit of land in Westchester, but not a heck of a lot. DEP land is worth a try and will probably be hunted less than other public land in the area. Hunting on private land would be the best bet, but I know it's not exactly easy to find a place these days even further north of the city.