RE: Sighting in / Target shooting on private property
I do not know about NY state, but I had a similar question when I took my hunter ed here in MA. The answer was given by a Mass Wild Life officer. His answer was that it is legal to do it but it is a bad idea. Some people (police, antis, etc.) might think we could be hunting if we are in the woods with a firearm.
Now I have shot on private property in Maine in an area that is sufficiently remote (and private) so I know it is not a problem. I also shoot air rifles in my backyard (out of sight from any neighbour).
I guess it depends how private and remote your property is?