Be sure to make reservations well ahead if you can as several of the coastal campgrounds book up in July & August.
Chesapeake Bay Bridge Tunnel is fine for RVs but if windy it closes to trucks & RVs also Propane is required to be off in the tunnels.
I assume you plan on spending the day in Wilmington NC ? The KOA Wilmington NC is inland from the beaches, Myrtle Beach Travel Park is on the Ocean and is only about 1 to 1 1/2 hours south depending on traffic. On Rt 17.
If you plan on traveling north to Wytheville VA, on I77 just a heads up Fog on Fancy Gap Mountain just in Virginia is common. Just in Virginia I77 MM1-10. Many pile ups. Worst was 90+ vehicles. Just heavy traffic otherwise.
Sounds like a great trip.