I took a walk on Beach Plum Island the other evening. It's one of the Delaware beaches I'd not been to before, and I wanted to have a look. It's very nice, in a quiet, remote sort of way.
Beach Plum is a nature preserve, managed by State Parks. It is a sand spit between the Broadkill River and the Delaware Bay. It runs south from Broadkill Beach to the Roosevelt Inlet.
There are opportunities for fishing, both in the Bay and in the River, and a calm bay-front beach.