Since I live in Orange County, my favorite thing to do is to travel all around L.A. I personally one day want to be a wandering journalist, like Anthony Bourdain, No Reservations, and just travel the world. This was taken a few months ago when one of my girlfriends' friend visited her from out of town.
If you haven't been to the Getty Museum in L.A, it should definitely be on your "to go" lists. (FYI: there are two Getty sites, one in L.A and one in Malibu). While you're here, you can roam around the garden, look at renaissance art and you can also sight see around the Getty: UCLA, Westwood, Malibu and Santa Monica.