In NY, STAY OFF the parkways and drive on the EXPRESSWAYS!
So as you come across NJ, it may be best to go a little north and cross over to NY on the George Washington Bridge (UPPER deck) to the Cross Bronx Expressway (over the Throgs Neck Bridge) to the Clearview Expressway which then leads you to the Long Island Expressway.
Bring plenty of cash for the tolls. If you can get an EZ-pass, even better.
Cross Island Parkway, Belt Parkway, Grand Central Parkway, etc. have very low clearance overpasses so stay off!
Also remember to talk like the locals. Say 'yo' and 'lon-guy-land'. Leave all "yalls" in Texas!