Where are the best farmer's markets in Los Angeles?

I can't speak for the entire Los Angeles area because it is such a sprawling place. But, if you are located near the South Bay, be sure to check out the Torrance Farmer's Market.Located at 2400 Jefferson St,Torrance, CA 90510 at Charles Wilson Park, the market is open on Tuesday and Saturday from 8:30-1:00. They have a large and varied selection of produce, including more exotic types of fruits. There is plenty of parking.
For more information visit their website:
(310) 781-7520
http://www.ci.torrance.ca.us/Parks

The best farmer's markets that I have found so far are at: Santa Monica - Main Street & Santa Monica - 3rd Street Promenade

My favorite Farmers Market in the South Bay is Veterans Park in Redond Beach on Thursdays from 8:00 am to 1:00 pm. Along with fresh fruits, vegetables, flowers, music they offer cooked foods. It's a great place to have lunch in the park with a beautiful back drop of the Pacific Ocean. Free Parking! For more
information, call (310) 372-1171, Ext 2252 ~ See you at the market!

Malibu is good and Burbank has a nice one on Saturday.

Every Sunday beginning at 1 pm , the Peninsula Center Shopping Center located in Rolling Hills Estates at Hawthorne Blvd. and Silver Spur Road holds a farmers market with fresh produce, flowers, and many other items. I even got my first dog here at an adoption event held here.

I like the Beverly Hills Farmer's Market. They always have great music. Twice per month, little kids can enjoy a petting zoo with pony rides. Their kettle corn is amazing and reasonably priced. Their produce is really nice, but a bit pricey. Parking is free. Once in a while you can even spot a celebrity.