On my next trip to the US, I want to go to a national part where there are mountain lions. I would like to make my own pictures of them. They are beautiful. I hear these animals are very illusive and widely avoid human paths. Yet, which national parks have them? I hope I will be lucky and see one.
"National parks" have a lot of people, which scares the lions away.
There are many lions up on the crest of the California Coastal Mountains around Big Sur, way up near the top. You can also try around Santa Cruz CA or south of San Jose CA, or west of King City CA in the Los Padres National Forest just to the north of the Fort Hunter Liggett US Army base.
Lions are elusive however, and they probably see you long before you see them, then they hide, or creep away. Lions do not want to be seen by humans. Humans are apex predators and lions know that.
The best strategy for seeing a lion is to ride a mountain bike along a trail at the crest of a coastal California wilderness area. Does not need to be a national park (there aren't any like that). Any California county park in the coastal hills would be a good place.
Over several decades of hiking and hunting I myself have only seen a handful of lions, and they all saw me first and started to run away before I ever saw them.