One of the great things about Los Angeles is that you don't have to go all that far to get away from it all. Buried deep within the Angeles National Forest lies Buckhorn Campground, just 47 miles from downtown Los Angeles. At 6,500 feet, it's a good 10 to 15 degrees cooler than the city, making it the perfect summer getaway (it's only open April through November). Between the enormous trees and the complete lack of cell reception, you'll forget that you're an hour's drive from Glendale Galleria. There's some great hiking along the Burkhart Trail, which you can take to Cooper Canyon Falls or to link up with the Pacific Crest Trail, which stretches from Mexico to Canada. At $12 a night, the 38 campsites are first come, first served, and be advised that the campground does get crowded on weekends, so you'll want to get here well before Friday evening if you're staying the weekend.
Take Angeles Crest Highway East, turn left at the sign. forestcamping.com/dow/pacficsw/angcmp.htm#buckhorn.