There's a list of state parks taking reservations here.

When not in a national park I tend to go to national forests and wilderness areas that never require or need reservations to camp - perhaps there are some of those regions within a reasonable distance you could look at? There are a ton of car/RV campgrounds around Huntington Lake in Sierra NF, for example, but one can easily drive out on some of the NF roads nearby and car camp in any accessible area for free.