The entire reservoir system is fishable.
Each res dumps into a tail water which leads to the next one. They are stocked heavily and wild, as well.
You may also fish the reservoirs themselves with a boat, or from the shore (I guess).
You will require an NYDEP permit to access this water as well as the state fishing liscense. Do not skip the NYDEP permit, as they heavily enforce it.
As for fishing on a res, obtaining a boat permit is much more convoluted. Each boat must be linked to a res, and you can't go from res to res without visiting a DEP station and having them powerwash and verify it. Boats are row powered only, no trolling motors and no gas. Bait has to be caught from each specific res and used in that res, as well. Not sure if that applies to the tail waters or not.