Your criteria of a close beach may eliminate
Topsail State Park, but if you could manage a walk across a boardwalk this is a fantastic option. We camped there several times with 3 kids and I must admit I felt like a pack mule carrying everything to the beach. Definitely a beautiful place, though.
'08 Ford F250 CC, 6.4L (stock)
'99 Ford Expedition (5.4L with tow package)
2005 Jayco 25G EXP