I have killed a day at LAX many a time.

Venice Beach I like very much. Sit outside in a café and sip a few beers or coffees, and it is the best people watching spot in the USA. Public bus right there. Get a few tattoos while you are there perhaps?

The other thing many overlook is the superb Getty Museum up in the foothills. Free admission and simply mind boggling art. Restaurant there too and again a public bus takes you right there for a buck or two.