One of my favorite state parks in the country, Assateague is sure to delight the whole family. This state park is near Ocean City, MD for touristy beach fun or near Chincoteague, VA for a more laid-back and nature-oriented vacation.
Assateague's claim to fame is being home to wild ponies ve roam on the beach and throughout the park. You're not supposed to approach them too closely, but they will wander near you on their own and make for some great wildlife viewing.
Additionally, Assateague is right on the ocean and has great, sandy shoreline without hordes of tourists. These are great shores to stroll and during low tide, you might find some small crabs and other critters roaming around.
Hike through the park, bike on the nearby paths, or camp for the night. It's a great place.