Cape Henlopen State Park is right up in the corner of Delaware by the ferry launch. Really pretty park, lots of hiking and biking. The campground is in the pine trees and they added some electric sites in the past 2 or 3 years. I've never camped there, but have visited the park many times. Not super easy access to the beach, but you can drive from the campground section to the beach parking lot and park for free. Easy access to Lewes, which is a pretty little town with a nice downtown area and a few restaurants and little shops. Fun little place to stay. Access to the more commercial Rehoboth Beach is a little more arduous. Driving is only about 10 miles, but its every bit of a 30-45 minute drive of frustration and red light. Its faster and straighter to bike through the Gordon Pond area about 6 miles to get to downtown.
A little further south is Delaware Seashore State Park. This is where we normally stay. It is a full hookup campground that is little more than asphalt road and pads in the middle of the sand. No shade, few amenities, but easy walking access to an isolated beach and short easy drives to Bethany, Dewey and Rehoboth beaches.
Since we go to the beach for the access to water and we enjoy walking and eating in Rehoboth we go to Seashore State Park.