Discover Pass in hand, cheap camping is available about 10 miles southwest of Olympia in the southwest corner of Capitol Forest. It's easily accessed, 6 miles west of I-5 at exit 95. Drive through Littlerock on Maytown Road (don't blink) and then take the Waddell Creek road to reach the two largest campgrounds in Capitol Forest.
I didn't check at Margaret McKenny, but there was NO Verizon signal at Middle Waddell, just up the road.
I wouldn't regard these as destination locations, but they are viable, accessible, cheap (no fee other than a valid Discover Pass) campsites near routes to the Olympic Peninsula and the ocean.