I'd try to go to Bethany Beach, DE, which is very low key and family friendly. I don't tent camp but there are several campgrounds up and down the coast, bayside and ocean side. If you are military, ex, DOD worker, National Guard, etc. you can camp at the Bethany Beach National Guard training site campground for $22 a night, in season. It's right at the beach.
Other DE state parks run about $28-$35 a night.
I took my five year old last summer and it was cheap regarding activities. He was thrilled just hanging at the beach. There is a playground in the middle of town, too, as well as a shaded one up the road a bit. I will post a link to that if you are interested in Bethany. He loved getting ice cream up at Hockers, an odd combo of hardware, grocery, and convenience store.
It's a sleepy little town without amusement parks. Some arcades. Some mini golf.
http://www.militarycampgrounds.us/milcamps/55-delaware/71-bethany-beach-training-site