If you do go to Broadkill let me know what you think. If you can't find anything there Slaughter Beach is just north and looks to be very similar. One word of caution: it is the Deleware Bay, not the Ocean, so if your kids are looking for waves to ride you need to go to Rehobeth.
Another amazing thing is the evening "electric fish" or whatever they are called. They are usually only visible at night late in the season. If you swim in the evenings in say August, run your hands quickly through the water and you will see glowing "tracers". These are actually tiny jelly fish with a lightning bug quality to them. It is amazing. I'd share the story about how a friend discovered them "back in the day" when his mind was, um, somewhere else due to something else but this is a family bored.