I’m not big on Cinco de Mayo. I dislike the fact that the day seems to be sponsored by beer companies and lots of non-Mexicans (and probably some Mexicans) believe it has something to do with Mexico’s independence from Spain. Not quite. Instead, the day commemorates the Battle of Puebla on May 5, 1862 in which General Zaragoza’s defeated French expeditionary forces. (More here on the origins of Cinco de Mayo.)
If you want to take part in some of the festivities around town, Noti Los Angeles has an excellent list of events. However, those who don’t know Spanish might have a little trouble reading about the different fiestas. Non-bilingual people can try Latino LA for another source of Cinco de Mayo events.