>>2515211Andy Arthur's website (
andyarthur.org) is a great place to start. He has probably camped on more public lands than anybody in New York and offers valuable information/maps on his website.
The state's Department of Environmental Conservation has a map with layers for primitive campsites and lean-to shelters:
https://gisservices.dec.ny.gov/gis/dil/ (switch to the "Outdoor Activity" tab)
Adirondack Park has 6 million acres with the crowds mostly concentrating in a few small areas (High Peaks and popular trails near Lake George and Old Forge). The Northville-Placid Trail goes 100+ miles through the heart of the Adirondacks. It has become a little more popular in recent years, but still offers tremendous solitude for the most part.
The Finger Lakes Trail is another good option for long-distance backpacking. Generally not too crowded except in popular spots like Watkins Glen and Robert Treman State Park. The map below shows camping spots, lean-to shelters, public lands, easements, closures, "branch" trails, and roadwalking sections (which you probably would want to minimize).
https://fingerlakestrail.org/plan-hikes-finger-lakes-trail/interactive-trail-map-segmented/CalTopo and Natural Atlas show public lands, campsites, trails, and other places of interest in NYS and elsewhere. CalTopo in particular has become my go-to resource for trip planning.
Dispersed camping is allowed in the state forests except where "No Camping" signs are posted. You just have to camp 150 feet (half a football field) away from any road or trail. There are also primitive campsites marked with a yellow disc where you can camp for free with no reservations needed.
May falls in the middle of "mud season" and is also prime season for ticks. Plan accordingly. I would recommend spraying your pants, backpack, and camping gear with permethrin. Tucking your pants in your socks also helps (it's a common tick-prevention measure here so you wouldn't look like a dork if you did this).