I camped at Holly Shores Camping Resort
in 2008. It's a few miles north of Cape May on US-9. You're not on the beach but the beaches of Wildwood and Cape May are close by. The site I had was roomy and the majority of sites are well shaded. There was a paved bike trail nearby that went all the way to Cape May. I had an enjoyable stay except for the mosquitoes- but that seems to be a problem no matter where you camp on the coast. I'd camp at Holly Shores again.
I haven't been to Cherrystone in a long, long time. But when I used to go there back in the 90's it seemed that each year, more and more campsites were getting converted into rental cabins.