What part of NYC? Technically, once you get halfway across the George Washington Bridge, you are in NYC.
The GWB is probably your best way to most parts of NYC, but if you want to go to Staten Island, you would need to take the NJ Turnpike and then one of the bridges into Staten Island. That might also be the quickest way to some parts of Brooklyn (those right across the Verrazano), depending on traffic. Also depending on traffic, you might be able to get to some parts of Manhattan faster by taking one of the tunnels.