The only campground that is in Cape May itself (it's actually in West Cape May) is
the Depot Travel Park. It is a very small,quiet but clean and friendly park. There are very few amenities (such as a pool) but you can very easily bike to the ocean, the boardwalk, or go anywhere in this beautiful Victorian city. The parks that others have mentioned are all full service and many amenities, with pools, lakes, some have mini-golf, etc. are actually located outside of Cape May (10 minute ride to Seashore Campground, 15-20 minutes between the others mentioned to Cape May. Our favorite is the Seashore Campsites but the others also have much to offer. Hope this helps!