EVERY WEDNESDAY - Rain or Shine!
This is not one of LA's biggest and best farmers markets, but it does the job. There are several stands, ranging from fruits/veggies, to breads, flowers, and even baby clothes. It's a nice place to grab lunch if you're into tamales or pupusas (I can't speak to the bbq or gumbo stands - but they look good).
There are a few benches to sit at - most shaded, and "free entertainment" provided by the old guy who plays harmonica and sings (charming, if not slightly annoying if your baby is sleeping).
There's not much for kiddos to do at the market necessarily, but there is a trackless train they can ride for $2 that goes around the park. And farther into the park there's an actual playground.
If you're in the area and you're looking to grab a bite outside or buy some produce, it's a nice place to stop by. Oh, and there are restrooms. I've never been inside, but they look decent from the outside. :)