If you are unfamiliar with the Adirondacks (ADK), the term "High Peaks" is the most talked about area for backpacking in the Adirondacks. They are the 46 tallest peaks in New York.
Jesse Black's link was great, its provided by the ADK tourism council. The "state government's authoritative" site is a terrible mess for the information you are looking for, but here it is: http://www.dec.ny.gov/outdoor/camping.html It gives a little more information about camping at specific elevations.
Check Trail conditions: http://www.adk.org/page.php?pname=trail-conditions
You might also find a lot of useful information from the Adirondack Mountain Club: http://www.adk.org/
Make sure you bring PAPER TRAIL AND ROAD MAPS. You can't rely on your cell phone for much of anything in the Adirondacks. There are towers near towns, but for the most part, you will be on your own! If you have a GPS loaded with new york maps it is very helpful!