CAN I camp ON NY STATE LAND LEGALLY?

Each park has its own rules. Check with the park offices.

you know that many people own land in the NY mountains, right? it's not all state land, you'd have to ask around for information on who owns what, what's private/no trespassing property, maybe ask for a updated property map for the location(s) you planning on camping in, because if you trespass on property, your going to have a very unpleasant night in jail on trespassing charges. if a property is owned by someone and they haven't posted no trespassing signs, you can camp there as long as they don't tell you to leave, the reason why I'm saying this is that they can't charge you for trespassing unless you refuse to leave immediately, if they try to, they're in the wrong. I'd find out who owns what in those mountains and ask permission to pass through and camp on their properties, as long as you promise not to ruin the property, they usually let you camp there unless they're doing something there(private camping, etc)