Natives are best, you can ask for them at a local nursery. Armstrongs has some. Home Depot too.

Your question is very broad as no one knows anything about your garden, parkways or lawn, sun exposure, size of plants which would be appropriate.

If you are new to gardening, I highly suggest you acquire a copy of Sunset's Western Garden book which will have suggestions for plants to use in arid gardens. Copies are sometimes available inexpensively at used bookstores which are often found at public libraries. My copy, which is 1995, has 7 pages of plants for arid gardens.

Also if you are new to gardening, you can look up your Sunset zone to see which plants would work best for you.

PS One other thing you can do is drive around your neighborhood and see what drought-tolerant planting has been done, see what you like, what has worked for others.

If you're looking for fruit trees, quince, pomegranate, and fig have more drought tolerance than most, but watch out, figs can have very extensive roots once it gets well established that can make it difficult to plant other things in the soil right next to it. Pomegranate is as decorative as it is edible, with fiery orange blossoms and big red fruits that look like Christmas tree ornaments. The hanging fruits of a quince can waft a nice fragrance throughout your yard, and the blossoms aren't all that less attractive than the tree's cousin (which is actually a different species), ornamental flowering quince.

Los Angeles doesn't truly have a desert climate but rather a Medditerran-type scrubland climate with mild winters and seasonal rainful. In terms of temperatures and precipitation, Los Angeles in the winter might be comparable to Maine in the summer.

If you're looking for an unusual one, can I suggest frankincense (Boswellia sacra), extremely drought tolerant, and the resin is valuable for incense

There are a lot of options for plant material that grows in Los Angeles. Feel free to check out my profile for ideas as I design in socal area.

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For fun do one "authentic"..Madagascar only. Mexican only.Or Australia only. Plants from the same habitat are happier with same plants as from the home climate. Or one side one continent...the other another.

Check out the Be Water Wise website for lots of ideas with photos. It's from the Metropolitan Water District Be Water Wise

The Water Wise website is perhaps one of the best resources available for your area, with extensive plant lists, tips on watering and establishing drought tolerant plantings as well as inspirational photo galleries. A second, similar website is California Friendly Gardening.