The state of New York has three main hiking areas: The Finger Lakes area, The Catskill Mountains, and the Adirondack Mountains. While the Finger Lakes and Catskills have their own charm, they are figurative appetizers. Your main course is the largest national park in the contiguous United States, the Adirnodack National Park. The Catskills may be known for adventures sports: Rock Climbing, Mountain Biking, etc but you can do these things in the Adirondacks as well, and have a much better view while doing them.
As far as day hikes are concerned, the Adirondacks have an immense variety of trails for all difficulty levels. Even within difficulty, there is quite a variety. If you don’t mind long hikes, but dislike steepness, there are plenty of trails that pass by various lakes and ponds. If steepness isn’t a problem, but you don’t have all day, there are quite a few tougher, but shorter climbs up mountains.
For Easier hikes, I recommend Goose Pond, Pharaoh Lake (approach from the south), and Snowy Peak. Goose Pond is a very short, very easy hike to a nice little pond in the Pharaoh Wilderness Area. If your vehicle can hand the dirt road that leads to the actual trailhead, the hike is only six tenths of a mile. Add another nine tenths of a mile if your car can’t make it. On the other end of the Pharaoh Wilderness Area is the southern approach to Pharaoh Lake. This hike is longer, but is relatively easy. Depending on which maps and signs you pay attention to, the distance to the tip of the lake is 3.5 miles or so. You can extend your hike by hiking along the water’s edge for as long as you desire. The lake itself is beautiful, and you get a wonderful view of Pharaoh Mountain. (To make this hike a moderate/difficult hike, climb Pharaoh Mountain while you’re there. It’s short, but quite steep and difficult.) Snowy Peak is a very short hike, but increases in difficulty the closer you get to the top. This is not for beginners, but considered easy, as experienced hikers can be up and down in less than four hours, and that includes lunch at the top. The views from the peak are gorgeous. The views from the fire tower are even better.
For moderate and difficult hikes, my recommendations would be Siamese Ponds, Avalanche Pass to Lake Colden, and Mount Marcy. Siamese Ponds fits nicely into the intermediate range. It is of average length, and mostly easy, but has some areas which are pretty tough. This trail is interesting as it changes continuously. Avalanche Pass to Lake Colden is a wonderful blend of rough and gorgeous. The views, especially at Marcy Dam, and anywhere cliffs can be seen, are spectacular. You need to fight hard for those rewards, though. This is a great test of one’s physical ability, and longevity. Mount Marcy, while not the hardest of the high peaks, is the highest peak in New York State. It is pretty hard too. The view from the top is great on sunny days, and, well, spooky on cloudy days. The enjoyment is in the journey, though. The trail is difficult and daunting, but so worth it, if you are able to complete it.
There are literally hundreds of trails to hike in New York State, and I’d be hard pressed to say I’ve ever hiked a bad one. These listed ones are just some of my favorites. Try these, and if you like them, seek out others, and enjoy.