Getting any gun in NYC is going to be tough...and an AR15 or M16 will be impossible. Disregarding that minor setback for a moment, a full-auto AR15 or M16 is going to run you serious cash - $9,000-10,000 bare minimum. You would have to form a corporation in a state like Pennsylvania which allows machineguns, and buy it through the corporation as a corporate asset. The gun would have to stay in that state unless you filed a form 5320.20 with BATFE to move it interstate, but if its to NYC or any end destination where the state or local law doesn't allow it, the form will not be approved.
For a semiauto AR15 you'll need to get a permit from the city to have the rifle in your home before you can even purchase it, but that won't be approved either. You can get rifles in the city, but hi-cap mags are not legal nor are most or the guns that take them. That said, I had a friend in Brooklyn who was able to get an HK SL8, but now you're back to more money than a cheap AR15.