Wenatchee National Forest campgrounds near Leavenworth [1] are generally open May to late October and charge $8–12. Get there very early on summer weekends or all the spaces may be gone! The closest to Leavenworth is Eightmile Campground (eight miles up Icicle Rd.). Six more Forest Service campgrounds are within 20 miles of Leavenworth along Icicle Road.
Another very popular Forest Service tenting spot, Tumwater Campground is 10 miles northwest from Leavenworth along Highway 2. Farther afield (16 miles northwest) is Lake Wenatchee, where you can pitch a tent at the Forest Service’s Nason Creek and Glacier View Campgrounds. Four more Forest Service campgrounds lie northwest of the lake.
Other, free campsites (with a Northwest Forest Pass) can be found driving from Lake Wenatchee up Chiwawa Valley Road, past Fish Lake to where the road turns to dirt. Unimproved campsites out this way along the Chiwawa River include Finner Creek, Riverbend, and Rock Creek, among others.
Showers are available at Oxbow Trading Post in Cole Corner (16 miles northwest of Leavenworth). Hiker and campers can also find hot showers and washing machines at Die Wascherei (1317 Front St., daily 7 a.m.–9:30 p.m.).
Links:
[1] http://www.moon.com/destinations/washington/north-cascades/leavenworth