Cherry Hill seems to be best for touring within DC attractions.
A potential state park for battlefield visits is Lake Anna State Park south of Fredericksburg. The Fredericksburg area has 4 major civil war battlefields plus numerous civil war and colonial attractions. Most fought over area of the Civil War. There is also a KOA at this same area. You could spend part of the time at Lake Anna and then move to Cherry Hill for DC touring.
There are two regional parks - Pohick Bay at exit 163 on I95 and Bull Run near Manassas on I66. Bull Run has full hookups. Pohick Bay has electric and water at the least. Both are south of DC but closer to city than Lake Anna. I don't think there is any service that offers rides into city for touring. Never had any luck finding info on available spots in the Metro Parking lots on either I95 or I66.
I volunteer at Fredericksburg military park but I have tried to be unbiased about all this. Although we live in Arlington, we have tented and RVed for about 40 years at most of the campgrounds (except for Cherry Hill).