If you want the lease stressful ride, yes.
Cross the Tappan Zee
Head south towards NJ, follow signs to the NJ Garden State Parkway.
Note, the Garden State Parkway (GSP) is the only "parkway" in the northeast you are allowed to take your truck or truck and trailer on.
The northern 40 mile section of the GSP has several arched bridges with low side clearance, typically 12'-13' on the shoulders. Some of the outer lanes are less then 13'6"
You will be fine if you take the bridges in the center of three lane sections or the 2nd-3rd lane of the 4 or 5 lane sections.
There are tolls and they all take Easypass.
There is a 22 mile section of the GSP below the Raritan River bridge that splits to local and express lanes. 50/50 on that.
Since the beginning of the express lane I have always avoided it. It's only two lanes and if there is an accident there is limited recourse for getting off the highway.
And another 2 hints.
Fuel is the same price the entire length of the GSP and the NJ Turnpike and will most likely be less expensive then what you are paying at home. Look at the rest stops as you travel south to see which ones look OK to you. The rest stop near the 130-134 mile marker is tight.
There is a rest area, fuel station just south of Exit - mile marker 100.
The Monmouth Rest area IS NOT RV FRIENDLY
The rest area was recently renovated and I swear they intentionally redesigned it to keep trucks and trailers out of the lot. We have been using it for over 30 years, and the last 16 years with RV's. I am leery of even attempting to access the GSP from the rest stop anymore, it is very tight.
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And very few areas to get out of Jersey with no toll with a bigger vehicle and trailer.