Within your distance requirement--or just barely stretching it--there are these possibilities in NorthEast Arkansas: Any of the COE campgrounds around Greers Ferry Lake would be a good choice.
Two state parks we have stayed in within that same distance are Jacksonport at Newport, AR; and Wooly Hollow, north of Conway. Wooly Hollow, especially seems to be the kind of park you are looking for, though it would add a few miles to your ideal.
If you have just a bit more time, you should consider Petit Jean State Park or Maumelle COE Park near Little Rock.
