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The Adirondacks are 5hrs away but are the undisputed king of /out/ land here. I meet plenty of people from that area who camp over the weekend, plenty of places to camp for free too.
Other than that there's a lot of smaller parks like letchworth, chimney bluffs, etc. There's a few long distance trails that go through the state, like the north country trail. Finger lakes region has a few nice trails around it, and wineries are a bonus.