The closest public campsites ($12 tents, $17 RVs) are in two county parks: Flowing Lake Park (10 miles north of Monroe, 360/568-2274, open year-round, no water in the winter months) and Lake Roesiger Park (12 miles north of Monroe, 360/568-5836, open mid-May through September).
Both of these parks have popular swimming beaches, and Flowing Lake has ranger-led nature hikes, along with Saturday-night amphitheater programs in the summer.
Park RVs ($10) or pitch tents ($5) during events at Evergreen State Fairgrounds [1] (360/794-4344).
Links:
[1] http://www.moon.com/destinations/washington/north-cascades/stevens-pass-and-skykomish-valley/monroe/evergreen-state-fairgrounds