San Jacinto Wilderness and San Jacinto State Park is my favorite local backpacking place in the warmer months. San Gorgonio Wilderness comes in 2nd.
I also like overnighting in the Cucamonga Wilderness coming up Icebox Canyon near Mt. Baldy.
For colder months:
Backpacking across Catalina Island is fun. You can make it as long or short as you want since there is a bus that goes across the island that will drop off or pick you up. The backbone trail in the Santa Monica Mountains is nice and almost complete, though the camping logistics currently sucks as you have to hike down to developed campgrounds. But plans are underway for backcountry camping in the future.
The Angeles National Forest has numerous places for a 2-3 day overnighter. It's Front Range (ie. lower elevation) near Mt. Wilson has some nice loops that can be put together and are usually below the snow line.
Easy Beginning Trips:
Little Jimmy backcountry campsite in the Angeles National Forest. Devils' Canyon in the San Gabriel Wilderness (located in Angeles NF).
Pick up the John Robinson Books: "San Bernardino Mountain Trails: 100 Hikes in Southern California" and "Trails of the Angeles: 100 Hikes in the San Gabriels" as these are updated every few years and have been the best resources for these 2 mountain ranges since the 70's.