Tapen Zee is the prefered way to get over the Hudson when compared to the GW bridge and cross bronx express way. If your goal is NYC, then something neat metro north or NJ transit is going to be easiest. You are not going to want to drive into Manhatten and first find somewhere to park a truck and then pay the ransom for said parking.
The only times I RV'd into LI was when I was up there for family.
2006 Ford F350 6.0
2014 Primetime Sanibel 3600
Enough other vehicles to not bother listing.
Previous RV: 2001 Monaco Knight