Beaches are easy - most people visiting DL actually go just a bit south of DL to Huntington Beach. Otherwise, LA tourists tend to go to Venice Beach (to see the quirky beach community and it's denizens that have made it so famous) and Santa Monica - for it's shopping and Pier amusement park - so you can see an original and what some of Paradise Pier in DCA is based off of.
Others go to Beverly Hills and Rodeo Drive to get a glimpse of the wealthy lifestyle, but you can see more real famous folks on Robertson Blvd - just a few blocks away. Or drive up to Malibu and go to the Country Mart shopping center after a trip to the beach there.
The museums are top notch too, if you love cars, the Petersen is amazing. The tar pits are an archeologists dream, and the Museum of Art is great. The science museum, down by the Colliseum, usually hosts one of the Body Worlds exhibits on a regular basis. Then there is the Forrest Ackerman Museum of Science Fiction - by special appt only. He is famous in the film community and has an exhaustive collection including the actual robot from Metropolis in his home.
Lots of amazing things to do in this area!