Boydton Va, Longwood park, When? The COE shuts down in October on this lake.
NC and Va state parks are open longer.
If doing Kill Devil Hills for the Wright Memorial, come up from Fl, and go to Okracoke NC, travel there is by ferry, and reasonable in cost or free depending on the route. Okracoke is a unique and quirky town, and everything can be seen in 2 days with free shuttle services.
Since you say military, visit Okracoke, take the pay ferry south to swans quarter and continue on south to Camp LeJune NC and even the AF facilities at Fort Fisher, nice quiet small coastal CG.
If you haven't seen it there is a website dedicated to
Military campgrounds which you may find helpful, in particular near Jacksonville, and Savannah.