I'd go to either Malibu or Dana Point for great ocean view beaches, or to Venis Beach to see the wierd, wacky, artsy and the beautiful people of So Cal.
There are the tourist attractions, Disneyland, Hollywood Blvd and the Walk of Fame (kinda seedy-trashy street though), Burbank for the Tonight Show, Melrose for the rich and infamous, Westwood for the Falafel and Stan's Donuts, movie premiers and plenty of the gay life, Rodeo Drive for the ultra riche.
Off the beaten path, there are literally tons of top restaurants, and great ethnic and everyday dives/restaurants, Pink's hot dogs, The Shack in Playa del Rey has a big burger that's a heart attack on the plate.
There's the Rainbow Room, great place to see Rock & Roll icons, and lots of LA women. Tons of live performances in the same area, great museum the Wilshire area.
There's the Hollywood Christmas Parade, huge event, also many of the surrounding communities have their own Christmas parades and events, Newport Beach Boat Parade for instance. Then there's Pasadena New Years Eve/Rose parade/Rose Bowl tons of people go there.
Griffith Park Planetarium puts on a great seasonal astronomy program.
LA is huge, it kinda depends how long you're gonna be there and what you like to do, and where are you going to be?
Good luck!