OK, so it isn't in the Finger Lakes Region. The Zoar Valley Canyon of Cattaraugus Creek is actually in Western NY near the town of Gowanda, roughly 80 miles south of Buffalo. Besides the canyon itself as much as 400 feet deep and with its knife-like ridges, the attraction is that many of the oldest trees in the northeastern U.S. reside in this area. It's in the Zoar Valley Multiple Use Area owned by NY State
A good source of information for exploring this area is wnyhikes.com/zoar/zoar.htm