I recomended these earlier to another member. Hope these give you some ideas.

Places of interest: Getty museum http://www.getty.edu/museum/, LaBrea Tar Pits http://www.tarpits.org/, and LA County Museum http://www.lacma.org/. Of course the beach would be fun to go to too.

Also, there is the Huntington Library and Botanical Gardens in San Marino http://www.huntington.org/. They have an great collection of art (It's where Pinky and Blue Boy reside) and the home and garden is out of sight.

For an inexpensive lunch, In-N-Out http://www.in-n-out.com/ is soooooo good.