Remote and obscure are the watchwords. If you have to get there by foot, that eliminates a lot of people. If it's not world-famous that helps too. Yosemite Valley would be the antithesis of what I'm talking about.
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It strikes me as odd, because usually taggers aren't willing to go all the way to Joshua Tree to do their tagging. The good thing is that it's federal land, so they can throw some outrageous resources at the problem to make an example out of someone. I recommend Predator Drones.
I went cross country skiing with my dad as a kid in Sequoia when Reagan was president and it was beautiful. I think cross country skiing is a magnificent way to explore our national parks away from the madding crowd.