The state of New York passes unnoticed for many tourists visiting NYC in the same way that Paris seems to rob tourists from the rest of France. That being said, the state of New York is a land of forests, charming cities, lakes, and vineyards that is worth exploring.
You can find this natural park of glacial origins in the Finger Lakes region of the north of New York. The trails are simple (but watch out for slippery parts!) and more or less flat. Perhaps the most interesting trail is the Gorge Trail (2.5km) which passes by 19 waterfalls, small lakes, and gorge-like rock strucures. If you want to check things out from above, I'd also recommend Indian Trail.