The Sespe Wilderness in the Ventura backcountry is close to LA. Plenty of opportunities to either hike on or off- trail. In the right places you can find large waterfalls, narrow canyons, hot springs, archaeological sites, fossils, pine forests, and on and on in addition to the officially designated wild and scenic Sespe River which runs through the wilderness area.
Fires are okay this time of year provided you pick up a free campfire permit. Typically open fires (and sometimes even stoves) get nixed sometime during the summer based on the very real fear of catastrophic brush fires. Anyway, you can either fax in the permit form to one of the Los Padres National Forest offices or I belive the Sequoia National Forest (not National Park) website has an option for a print-out campfire permit provided you pass their fire safety quiz. The permit is good for the calendar year and is valid in all National Forests. Collecting deadfall for campfires is fine in the LPNF although they encourage you to use established campfire rings.
EDIT: Just to clarify a little on the established campfire rings comment: All (or most) of the official backcountry campsites have fire rings/pits. You'll also find many "unofficial" campsites that don't show up on maps but have fire pits. I tend to believe these are fine to use. If you set up camp in an otherwise "untouched" spot, I'd just encourage you to practice LNT methods. I have a few "hidden" campsites where we've built stone pits for a fire, but we dismantle them, scatter the ashes (once they're fully out) and generally cover our tracks to leave the place more or less how we found it.