I love to mountain bike, and the Adirondacks have many great places to bike. However, there are also many restrictions regarding where you can mountain bike. As a general rule, trails in "Wilderness" areas are restricted to foot travel (or horses in some areas, but not bikes). This includes nearly all trails in the High Peaks Management Unit.
In my experience, even hiking trails that allow bikes are not the most enjoyable rides--- trails that are designed for foot travel are not the best bike trails. The best riding that I have found is on old logging roads, fire truck roads, and back roads. These are open enough to permit reasonably efficient travel by bike while allowing for some great scenery and minimal carries. Another option is some of the abandoned stretches of the Adirondack Railroad.
For the Shutterbugs:
I created this photograph by clamping my Nikon onto my bike frame using a Bogen Super Clamp.
A 20mm wide angle lens and a slow shutter speed of 1/8s completed the setup. I would start pedaling on the trail
and then trip the shutter which was set on timer to allow me time to get set for the photo. The slow shutter speed
causes the blur which gives an impression of speed as the bike careens down the trail. Nikon F4, Nikon 20mm lens:
f22 for 1/8s. Film - Kodak Lumiere, ISO 100.