Jersey City

Between Assateague and Jersey City on the major highways there are no tunnels and no height restrictions that I know of. There are two possible routes I would consider.

1. Pick up route 113 at Berlin and head north to join with route 1. You want the Delaware Memorial Bridge, which is the southern end of the NJ Turnpike (I95). IIRC, our GPS had us get off route 1 onto route 13 to join I295 to go over the bridge. I'm pretty sure you need to get off the Turnpike near Newark Airport onto I78 to get to Liberty Harbor, but since we haven't been there your GPS should know better.

2. When we come home from Assateague, we like to take the Cape May/Lewes Ferry. The ferry is a 90 minute ride that you and the kids may enjoy. Check the cost for your rig.

We head north out of Assateague and drive through Ocean City and on up the coast on route 1 to the ferry (watch signs). From the ferry it is easy to get onto the Garden State Parkway (RVs allowed). The parkway joins with the NJ Turnpike at Woodbridge.

X2 on what cloud driver said.
I love the cape may-lewes ferry, though it is quite $pendy!
I recall you saying a while back how the kids want to see dolphins, and the ferry is a great place to see them 90% of the time I been on it. Plus it gives u an hour and half or so break at the wheel.
Do your best to AVOID arriving in jersey city between 7:00-10:00 AM and 4:00-6:00 pm

Follow up...assuming you do the ferry into jersey, you will be on the parkway 129 miles then major interchange onto Turnpike for about 15 miles to route 78 east which is kind of still part of the turnpike at that point. Not even a mile of local street driving once off route 78 to get to a Liberty RV. I can't stress to you enough that that place is truely little more than a parking lot with hookups. Imagine a Walmart parking lot with water and electric, but no store.

All I could afford wrote:
Follow up...assuming you do the ferry into jersey, you will be on the parkway 129 miles then major interchange onto Turnpike for about 15 miles to route 78 east which is kind of still part of the turnpike at that point. Not even a mile of local street driving once off route 78 to get to a Liberty RV. I can't stress to you enough that that place is truely little more than a parking lot with hookups. Imagine a Walmart parking lot with water and electric, but no store.

Your description is correct but it is clean ,safe, and has great access to public transportation into NYC

I would follow the directions you have to the Cape May - Lewes Ferry and then the Garden State Parkway, as noted, up to Exit 129 for the NJ Turnpike. I-78 is the Newark Bay Extension of the NJ Turnpike at Exit 14. After paying the toll drive straight until you come to the first stoplight. After the first stoplight begin to merge to the farthest right lane. At the last stop light before the Holland Tunnel, make a right onto Marin Blvd. Follow this road until it ends; the office is on the right. - See more at: http://www.libertyharborrv.com/directions#sthash.NaIqZAMo.dpuf

Marin Blvd. is a snug urban street, but quite do-able. Try to catch the view of Lower Manhattan at sunset from nearby Liberty State Park.