I did a radius search in MS Streets and Trips using 25 miles out with Fuquay-Varina in the center. Other than the aforementioned State Park and the William B. Umstead State Park, the only other campground in that radius was a Holiday Trav-L-Park 24.9 miles (as a bird flies) out.
Not sure if it'll meet your needs but here's the info on it:
<span class="ev_code_GREEN">Smithfield Best Holiday Trav-L-Park
497 Hwy. 701 S.
Four Oaks, NC 27524
<span class="ev_code_RED">I-95 (Exit 90) 300 yds South on Hwy. 701.</span>
'11 GMC Acadia SLT AWD
'11 GMC Sierra 1500 4x4 Extended Cab