Southern Va means Virginia Beach south...you'd have to drive through
VB to get to the Eastern Shore. Not worth the effort.
I have spent time on the East Coast. Hatteras is good, OBX in September has charm.
I prefer, as suggested earlier, Atlantic Beach. New Bern is a great town, have dinner there or stay there and drive to the beach for the day...I flew out of Cherry Point enough to get smart about where to go.
Pawley's Island, SC seems more your style, frankly, probably worth the extra hour or two in the car.
https://www.townofpawleysisland.com/
https://www.pawleysislandrealty.com/
I have also stayed in Myrtle Beach in the off season...if you push your trip into October, the deals are great.