May I, as a former resident of that beautiful state, relate to you a true story? It is one that a friend of mine told me over lunch one day in the early spring of 1995. We were at my house in Potsdam in the north country area and this happened to her in Norfolk just a few days previous.
My friend was gathering some roots and spring time herbs when nature called. She made for an isolated spot in the bushes to rid her bladder of her morning coffee. She heard some rustling to her left. Still squatting, she turned and looked up.
There, not more than 3 ft. in front of her was the nose of a young moose sniffing at her through the brush. My friend was so astonished as the sight, all she did was heard herself saying, "moose."
It was about that same year that an Amish family in the area had to pay a $1000 fine because their teenage son had accidentally shot a moose while deer hunting.
Now, those are both true stories of moose in NYS. You don't know me and you don't have to believe me but I, for my part, have no reason to lie to you. Google easily provides links to other stories. Here's just one such link that includes pictures: Adirondack Moose Central
As for wolves, I have my own views on their place in the eco-system and don't care to get into that part of this thread. (even though it is the main topic here, sorry y'all) These types of threads usually devolve, as this one has, into somewhat of a pissing contest with neither side convincing the other of their POV.
But as to coyotes in my home state, since I am not sure of the particular legality issues surrounding the shooting of a coyote that wanders too near your chicken coop, I'll not tell you any stories of a person I may or may not be related to who lives in the scenic region of lower Canandaigua Lake. I will instead urge you (along with more than one other poster here) to avail yourself of the wonderful resources at your fingertips and verify your assertions before posting.
See #77. I incorrectly had it in my head that the original poster was talking about NY City, instead of upstate NY like he meant.