I second Andy Guest/Shenandoah River State Park in Virginia.
I will also suggest
Janes Island State Park in Maryland. While not on a river - it is on the bay - they have some great water trails. One can kayak to a deserted beach in the Chesapeake Bay and enjoy the day.
Point Lookout State Park is another great kayaking/canoeing park in Maryland with a lake, the Potomac River, and the Chesapeake Bay available. The campground has full hook up sites in the woods or electric sites on the water. An excellent place in October...
And don't forget Assateague - canoeing/kayaking is great bayside, though not a river.
