From Mima Mounds [1], continue north on Waddell Creek Road to Capitol Forest, a multiuse working forest (look out for logging trucks) in the Black Hills. The hills received their name when early Anglo settlers found the entire area had been charred by a forest fire.
Free primitive campsites are available for tents and RVs at nine locations within the forest; many miles of hiking and horseback riding trails are clustered at the south end of the forest, while fat-tire bikes may roll along those in the north end.
Links:
[1] http://www.moon.com/destinations/washington/south-puget-sound/olympia/sights/mima-mounds