I do not know if you can make a (legal) beach landing but you could checkout sailing the Delaware Bay to Lewis, and possibly stay at Cape Helopen State Park. It's about 12 miles from Cape May to Lewis. If you started up the bay around Reeds Beach it would be about 25 miles, (straight line). You would need to explore the possibilies on the Delaware side first. Also be aware of the strong current and shipping in the Delaware bay.
I don't know anywhere that would permit beach landing and camping on the beach in New Jersey.
'79 Hobie18 - Magnum