Eight miles west of Burlington on Padilla Bay, Bay View State Park (360/757-0227, www.parks.wa.gov [1]) has year-round campsites for $13 ($19 for RVs) across Bay View-Edison Road from the waterfront. Make reservations ($7 extra) at 888/226-7688 or online.
Additional campsites can be found at Skagit County Fairgrounds (360/336-9453), on the corner of Hazel and Virginia in Mount Vernon [2].
Private RV parks include Burlington KOA (646 N. Green Rd., 360/724-5511 or 800/562-9154, www.koa.com [3]), Riverbend Park (305 W. Stewart Rd., 360/428-4044), and Mt. Vernon RV Park (1229 Memorial Hwy., 360/428-8787 or 800/385-9895).
Links:
[1] http://www.parks.wa.gov
[2] http://www.moon.com/destinations/washington/north-puget-sound/skagit-valley-and-mount-vernon
[3] http://www.koa.com