Happened to be skulking about the forums and noticed this thread and figured I'd rise from the dead to answer.
If you're wanting right near the airport, I'd recommend either Ballona Freshwater Marsh or Madrona Marsh. Both are pretty urban, but they have a lot of the common California specialties/western species such as Anna's and Allen's Hummingbirds, Bushtit, California Towhee, Hooded Oriole, etc. If you're willing to drive a bit, I'd check out some stuff in Orange county. Bolsa Chica Ecological Reserve and Huntington Central Park are near each other and can easily be done in a quick morning. Bolsa Chica is excellent for waterbirds/shorebirds (though the latter will be really limited this time of year). There's a large Elegant Tern colony, as well as Least, Forster's, Royal, and Caspian Terns, Black Skimmer, etc. Ridgway's Rail is possible but I've had bad luck with this species here in recent years. You will get a handful of common landbird species, but Huntington Central Park is better for that. Huntington Central was better in previous years, but you can still pick up easy, common species here. Shipley Nature Center is in the western half of the park, though it has really weird hours (off the top of my head I can't recall them). I typically bird the eastern half of the park in a clockwise manner, starting near the Park Bench Cafe. Common species here include Anna's and Allen's Hummingbird, Nuttall's Woodpecker, Black Phoebe, Western Bluebird, Lesser Goldfinch, California Towhee, Hooded Oriole, Great-tailed Grackle, Scaly-breasted Munia.
If you're willing to drive even a bit further, there's a lot of places you could check out. San Joaquin Wildlife Sanctuary is always good--basically the same species as Huntington Central, but better chances for all of them, more species, and it's a nicer area to bird.