The Catskills region of New York state, along with its more northerly sister range, the Adirondacks, contain the oldest wilderness areas in the country (set aside in the late 19th century) and some of the most famous fly fishing streams in the United States. What American fly-fisherman hasn't heard of the Beaverkill, the Willowemoc, or the Ausable? These are the waters where many of the basic techniques we now associate with fly-fishing were invented.
IMO (and I recognize I'm in the minority), the famous streams are today way over-rated. Most stream frontage is posted. Places where you can gain public access are crowded. And to sustain the fisheries in the face of intense pressure, they are heavily stocked.
But if you're willing to hike into the back country a bit, you can discover a very different New York. A state with enormous reserves of wilderness and park land, which is far enough north to support trout habitat in most areas where the watersheds are reasonably intact. The stream depicted here is one I fish semi-regularly. It's nearly two hours closer to NYC than the storied Catskill streams, yet receives relatively little fishing pressure. It holds wild brown trout, which average about 8".
Check out the data on this site, and you may discover places to fish you've never considered. And, if like me, you're sick of standing cheek by jowl with aggressive New Yorkers who don't know any better, it may open up a whole new dimension to the sport.