I run a league at UCLA, about 6 miles away. That's the only one showing up at pokemon.com. We're pretty small, averaging about 6-8 people per meeting. Details and my email are here:
http://www.pokemon.com/us/organized-play/leagues/3463/
There's a store called Toy Mandala that advertises Thursday nights as Pokemon nights from 6-9pm. It's in the Westside Pavilion mall, at the corner of Pico and Westwood. I've never been, but someone from my league who went said that it's also small, about the same size as us. This one would be closer to Marina Del Rey, but you should contact the store since it's not appearing on the Pokemon website. Their contact info is here:
http://www.toymandala.com/contact.html (you want the West LA store).