I have lived in NJ my entire life and will tell you, once you get past the middle of the state either via the parkway or the turnpike a MH or TT is not something you want to have. If you pull off one location you can be stuck trying to turn around. Your best bet to stay someplace below route 195 on the east cost and take a bus up to the the city. It's the cheapest way. Getting over the bridges and tunnels is costly, parking is another nightmare. You would be lucky to pay $20 per day and that's for a car. Most places are not going to be able to handle a MH TT. Also low overpasses could be a major problem but if you stay on the interstates you will be fine as trucks are constantly on them.
Do not stay here
Surf & Stream Campground. I live right down the road from them and even though the website looks great. The park is pretty much a fulltimer park. Many of the MH are covered with tarps to prevent water leaks. I have drove into it just to see if it would be a nice place to stay for a 5 min drive and well as I said I would not stay there.
Cedar Creek Campground
This place looks really nice. About 10 mins from me and my sister has stay there. She says, it's clean, friendly and very nice. Also you can catch a bus about 5 min drive north on route 9 that will take you directly into NYC. From that route you would not have to worry about low clearances as there are none. Also you could from that location, if you decided to drive the MH to the beach (about 15 mins east). If you or anyone in your family is military, active, retired, guard etc. Island Beach state park is beautiful and you can get on for free. But that beach fills up fast and they close the gates about 1030 am. That is a really nice beach, you would think you were in Mexico not NJ.
As for any northern locations Liberty Harbor in Jersey City is the place. It's not that hard to get to. But keep in mind their only selling the location to get into NYC. If you decided to do something else you would have to leave. But what is nice, is that everything is right there. Statue, park etc. It's a fast paced trip, hustle and bustle. If you look up that park on google and go to images you will see it's pretty much a parking lot with W/S/E. very close parking.
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