The lakes in SoCal are either private property or part of a state park system, they have boating and jet skis, but I would not swim in them. they have viral things that swim up your woohoo. Lake Elsinore, Lake Hemet, Lake Fulmor, Big Bear Lake, Lake Arrowhead, Piru Lake. Nice to photograph and hike around, but gross to get in the water.
Hammocks, you probably can, but I just don't see any body doing it in the national forests. probably our trees are either burnt, weak from the fires, or bark beetle diseased, and the hammock roping will probably strip the bark and expose the tree to further disease. Just my thoughts.
you need a free entry permit usually, and an adventure pass (parking $5 per day / $30 annual)
Some state parks are connected to the national forest. the SP charges a lot of money, the NF is close to free. same mountain, different entry points different costs.
if you want to drive 3 hours, you might as well drive 5 hours and head up to Sequoia / Kings National forest - eastern Sierras. now that is a different experience, a different California.