if you go back over the border to delaware county north of 17 between exits 82 and 89 there is a great deal of state land around in that area not including the new york city land just plain state land where you do not need a permit to access.
check out the ny dec wep page. they have a complete listing of all the public hunting area's and any info that you might need in regards to permits or any special rules
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ranger's lead the way all the way