Hello Mustang, welcome to the forum.
I just went through the same this past fall. I spent almost 4 months looking and researching before I even settled on what to go after. Then it took almost 2 more months to find what I wanted at reasonable enough prices. Check out the classifieds/vendors on here as well as,
GunBroker.com Online Gun Auction
What I have found out is to own an AR15 in NY,
There is a difference in the regulations for Pre-Ban and Post-Ban rifles. A pre-ban rifle is one that was manufactured prior to the 1994 Assault Weapons Ban. A post-ban is one manufactured after the 94' AWB. The major differences are,
1. Bayonet mounts - pre-ban rifles can have bayonet mounts. Post-ban rifles cannot.
2. Collapsible/adjustable stocks - pre-ban rifles can have them. Post-ban rifles can have them provided the stock is permanently pinned in a fixed position.
3. Flash hider - Post-ban rifles must have the flash hider permanently pinned to the barrel.
4. Magazines - currently in NY you may not purchase magazines with greater than 10 round capacity. You may have magazines of greater capacity provided they were manufactured prior to the 94' AWB. These would need to be stamped by the manufacturer.
You may also want to check the following links for official information,
ATF Online - Bureau of Alcohol, Tobacco, Firearms and Explosives
Firearm Laws for New York
gunlaws.com / Bloomfield Press
Official National Rifle Association of America Home Page
Gun Owners of America
As for the Colt LE6920 it would not be legal in it's advertised configuration. The stock would need to be pinned and you cannot have the (2) 20 round mags. I can't tell but if it wasn't than the flash hider would also need to be pinned.
And don't forget to post up on your progress. You may also want to join up as a supporting member - the forum comes with loads of information and support.