i have a house/land not to far from there,
just east of Wtown near ft drum,
you have some great lands near you
Tug hill region has lots of state lands
try looking at DEC site for jeff county,
look for state forets and WMA,
looking for just one, might miss the other,
there are tracts of just a few thousand acres to +50k acre state lands, many conjoining giving you +100k acres of state land to hunt,
lots of maps and info on ny dec site
can also try this
http://www.dec.ny.gov/outdoor/45415.html