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Where in Socal?
For hiking theres Mount Baldy (no permits). Mount San Jacinto (self issue permits) and San Gorgonio (permits must be reserved in advanced). Camping (overnight) for San Jacinto and Gorogonio must be applied for ahead of time.
Joshua Tree if you like bouldering / rock climbing, not too sure on permits there. I think theyre pretty easy to get and only needed for over night. There is Kern Area which is known for river activities, no permits (not sure but Ive never used one). There is Mojave desert and Red Rock, which is where I go shooting.
3 hours north of LA, is Mount Whitney, and the surrounding Sierras. But those need permits. Langley and Williamson are easy to get though.