Be prepared for plenty of traffic on I-95 in Conn. and New York and the GW Bridge. From that point, I-95 will be the NJ Turnpike. It looks like your route has you exiting and picking up US 1&9 to Marin Blvd. It's doable, but heavy city traffic, narrow congested streets and stop lights.
I'd suggest going a little further South on the Turnpike and take the Northeast Extension to Exit 14C. After the exit toll both, you will be heading for the entrance to the Holland Tunnel and will be in about 8 lanes of traffic. Make your way to the right lane as soon as possible and watch for Marin Blvd. as a cross street. It's close to the tunnel entrance. From there, it's, again, a narrow city street, but straight into the campground in about 2 or 3 miles.
Stay away from anything called a Parkway in Conn. or NY. The Garden State Parkway in NJ is okay.
