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highly rec going to a spot called Willow Hole. the hike is v easy, save for some walking thru sandy washes. it ends at a nice spot with awesome rock formations, trees, and maybe some water if you're lucky. you can scramble all over the place and explore to your liking.
i've stayed at Ryan and Cottonwood Springs campgrounds before. Ryan is better as far as scenery goes, but there's a dope hike to Lost Palms Oasis that starts near Cottonwood Camp, which i also highly rec.
Lost Horse Mine has some p great views, as well.
Joshua Tree is a great park. You'll probably see lots of people, but like other popular parks, you can escape the crowds by actually hiking a few miles down a trail
i definitely prefer the high Mojave Desert to the low Colorado Desert. both have their charms, tho, and since you're gonna be there a while, check em both out!