Sorry for the late reply. Did not see the post. As far as NJ is concerned there are not camp sites that offer beach camping here. Sandy hook, (north of LBI) does offer camping but it's tent only. Most of the camp grounds I have seen here below LBI are decent. Just call them and ask if they have full timers. Many of the places here call themselves "resorts" when in fact they are a trailer park. There is a difference in resort place that caters to vacations then a place that has income with full timers. Property taxes are very high here so a camp ground with 20 acres could be paying up to 6 figures a year or more in property taxes and that's a hard nut to crack at the end of the year.
I've heard good things about these places.
Sea Pirate Campground
Brookville Campgrounds (stayed here, it's not bad, direct route to LBI beach if you take a left out of the park)
Chestnut Lake RV Campground (looks like a nice place)