There are three gardens that are pretty much in the immediate area and all three are worth visiting:

Descanso Gardens is located just a few miles away. Your timing is pretty good because Descanso is famous for several acres of Camelia forests which are just coming into bloom beneath a canopy of tall Oaks. They have other gardens as well.

Huntington Library and Botanical Gardens is a must see and is located just south of Pasadena which is also nearby. It's pricey but well worth the visit. It's in my opinion the best botanical garden in CA.

The Arboretum and Botanical Gardens of Los Angeles County(located in the city of Arcadia)is also pretty close and worth visiting. Their website or server was down when I posted this and thus I'm unable to provide you with a link. - Mike

In Downtown L.A. and nearby, there's the James Irvine Garden in Japantown, Grand Hope Park (with lots of outdoor art), and Exposition Park (with a fabulous rose garden).

In the Midtown District, there's MacArthur Park (where someone left the cake out in the rain) and Lafayette Park (with a scented garden).

In Beverly Hills, there's the spectacular Cactus Garden and the Virginia Robinson Gardens (call ahead).

On the westside, there's the Self-Realization Fellowship Lake Shrine, the UCLA Hannah Carter Japanese Garden, and the Mildred Mathias Botanical Garden.

In the San Fernando Valley, there's the Orcutt Ranch Horticultural Center.

Near Griffith Park (a HUGE garden unto itself), there's Echo Park and Elysian Park (including the Chavez Ravine Arboretum).

In the Burbank/Glendale area, there's Descanso Gardens (a MUST).

In Pasadena and nearby, there's Eaton Canyon Park and Nature Center, and the Huntington Botanical Garden (an ABSOLUTE MUST).

East of Burbank, in the San Gabriel Valley, there's the L.A. Arboretum (another MUST).

In south/east L.A., there's Hollenbeck Park, Lincoln Park (300+ species of trees), Heritage Park, and Whittier Narrows Nature Center.

For a longer drive, if you want to go south down the coast, there's Burton Chance Park and the South Coast Botanic Gardens (with a great butterfly garden).

Disneyland (in Anaheim) is quite the botanic garden itself. Call ahead for a behind-the-scenes plant tour.

Joe

The Japanese Garden in Van Nuys is between Burbank and Canoga Park. It doesn't take too long to see, but it is neat. Check out their website: www.thejapanesegarden.com

The Japanese Garden
6100 Woodley Ave,
Van Nuys,California, 91406

Wow! I am so excited to have this many choices.
Thank you all very much for the information.

You are very lucky to have so many beautiful places to visit - not to pick on Florida, but we have very few here.