Not the classic beach with a boardwalk experience, and a little bit further, but very family friendly, plus ponies: Chincoteague, VA
I’ve always wanted to do the annual “Walk across” day. Although I worry that I might freak out when it starts to sway. . .
I’ll call and raise you Assateague Island, MD (either National Seashore or the Maryland State Park)). About 15 minutes from Ocean City.