Catch a Dodger's game.
Griffith Observatory.
L.A. Science Center, they have a Space shuttle and a humongous fuel tank.
Getty Villa in Malibu or Getty Center (West L.A One), but Villa > Malibu.
Huntington Library, then some amazing Chinese or Vietnamese cuisine in San Gabriel (check out Yelp, tons of great places)
Broad Museum and then get food in Downtown L.A. (Grand Central Market, Sushi in Little Tokyo or Korea Town (K-Town sushi is as good as Sawtelle or Little Tokyo Sushi for a lower price), Howlin' Ray's Fried Chicken, Bestia, etc.)
If you drive South, San Diego is really laid back with tons of good food and nightlife.
If you head North, Cambria, San Louis Obispo, Half Moon Bay, Santa Cruz, Big Sur, Redwoods state park, etc. Are all beautiful you can rent a bike or hike.
If you like fish, you can't go wrong eating Pescado Zarandeado my favorite fish dish. It is grilled Snook, sold by the kilo and grilled over charcoal. (Cheko el Rey del Zarandeado, Mariscos el Kora, Mariscos Nayarit, and my favorite Coni Seafood).
Tacos, Tijuana style tacos are the rave atm. Grilled asada, handmade tortillas, cheese thrown on the grill, and Guacamole/onion/salsa). The tortilla is used to pick up the now crisp yet rich cheese, then the asada is added, and a scoop of guacamole. You can added onion cilantro and salsa.
They are good but I prefer, Tacos al Vapor. The meats are steamed and fall apart. Get cow head, cheeks, or lip so tasty and beefy flavor.
Birria tacos are also gaining popularity. Some people call them red tacos because they use the red liquid released when preparing the meat to make the tortillas.
I'll list some taco spots later today.
Enjoy your trip.