I'm originally from Orange County, about an hour south of LA. Honestly, I tried to go to LA as little as possible since traffic was always a pain. Are you talking about the city of Los Angeles only, Los Angeles County or the LA area in general?
I've been out here for several years, so my geography is a little fuzzy. If you need things in LA city, check the locations of Hollywood Blvd., Rodeo Drive, Universal Studios-Hollywood, the Hollywood sign, Malibu, the Getty Museum, the Los Angeles Zoo, Griffith Observatory, the La Brea tarpits, Venice Beach.
Down in Orange County, which would be considered part of the LA area in general, there is of course
Disneyland. San Juan Capistrano Mission is one of the more popular of the California missions because its the one the swallows return to each year. There is also the Aquarium of the Pacific in Long Beach and Catalina Island. If you're covering all of Southern California, you have to include the San Diego Zoo. It's one of the best in the world. But, it's too far to be considered part of the LA area.
As for events: Rose Bowl and Parade in Pasadena. I'm sure there is somethig for Cinqo de Mayo as well, but I can't remember anything specific. The Glory of Christmas and the Glory of Easter every year at the Crystal Cathedral in Garden Grove (Orange County). Knott's Scary Farm at Halloween in Buena Park (also in Orange County).