Have spent many years camping in the Wildwood/Cape May area. IMHO, the very best campground down there is Holly Shores Campground on Rt 9 between Wildwood and Cape May. Only 10 minute drive to each! Very big park, shaded sights, great for kids with a huge pool, playgrounds, organized activities. Very clean and modern restrooms, showers. Have been going there for 35 years. It is rated #1 in NJ! Full hookup sites. However, it is not cheap! You will need to make reservations right now for July. Pull it up on line for more details and CG map of sites.
Regarding beaches, Wildwood Crest is the nicest! Huge wide beach, never a problem finding a private spot to put your stuff The ONLY beaches in NJ that are FREE are Wildwood and Wildwood Crest. Extremely clean and groomed daily! If you want the whole boardwalk and amusement pier scene, that is in Wildwood. 4 large fun piers, hundreds of eating places on the Boardwalk. Very clean, mostly "family" atmosphere. Not dirty and dangerous like Atlantic City-- As others have said, unless you just want to gamble, do NOT go to AC for any other reason. It is a real scumbag town and you will not feel safe!
As others have said the Cape May zoo which is free is amazing! much bigger and well done than you would ever expect in a small town! Do not miss it!
Enjoy the Jersey shore!