There is the Upper and Lower Lakes WMA outside of Canton.
WMA Link As well as the Brasher National Forest, around Brasher New York. The Brasher Forest and the Upper and Lower Lakes hold alot of whitetails, but the hunting can get pretty heavy at times. The Adirondack Park also extends into Franklin and Saint Lawrence counties, the Santa Clara Tract offers access to some public lands, though the deer population has declined there in recent years. If your wallet is fat there is the Lucky Star Ranch, not too far from Alex Bay.