Well, if you want to head into the ADK's, ther are a few options. The Nothville-Placid trail is about 135mi long. It takes about 9 days to hike it. If you do any fishing,about two weeks.
The Trans Adirondack Route follows the NPT for a ways. Or, you can string a couple trail together to do some peaks in the High Peaks Area between say the Heart Lake Loj and Keen Valley. There is no difinitive route for the North Country Trail through that part of NY.
The Moose River Plains offers a lot of hiking in and out of the many lakes in that area with connections to the NPT and NCT. The road is never good getting in and out. If you enjoy backwoods fishing, the fishing is fair. A canoe, raft and/or float tube is almost maditory for the hundreds of lakes.
If you enjoy canoeing, it is about as good as it gets. The St. Regis is nice, Oswagatchie, Cedar River, etc. More'n I care to mention. There is a LOT of water. The Northern Forest Canoe Trail goes across northern NY from Old Forge to Plattsburg. Saranac Lakes, and Fish Creek Ponds can be offshoots. Lots more.