Maybe look in the Malibu Canyon area, best of both worlds if you want Mountains but still a short drive from the beach. Malibu Creek State Park is cool, especially if you can find the hidden backtrail swimming hole.
However, I prefer the Angeles National Forest. It's more rustic camping and since it's farther from the city there aren't as many day-trippers. There are cool places off of Hwy 2. Its much more mountainous and more densely wooded. There are creeks and rivers all through there and several good campgrounds, and the campfire restrictions are generally more lax. However, it's a decent drive to LA proper from there so it all depends on what else you plan on doing.
There's also Mount Baldy area, in the IE just east from LA. Awesome up there but the beach is well over an hour away.
Options are vast. Use Google maps creatively and you should be able to find something cool. First, find an area that looks like mountains then search for camping areas. Use the directions tool to figure out the distance to other desired locations. Also keep in mind that driving through LA you will definitely not be able to use the '60 miles:60 minutes' rule. You can hit deadlock traffic at weird times like 2:30pm on a Tuesday so give yourself plenty of head-time when going anywhere.