While it may seem like the best solution to rent a car (and if you do, there's a service called Zip Car that charges hourly), keep in mind that Los Angeles is host to obscene amounts of traffic and terrible drivers.
Las Vegas is fun. Excellent gambling, but go hotel-hopping if you can (this just means you walk around every lobby of every hotel of the main strip).
San Diego Zoo is a MUST. And Sea World.
In Los Angeles itself, try to go to Olvera Street, Universal Studios, Six Flags, and a few art museums like The Getty if you're that type of person. Not much to do in Santa Monica apart from the pier and 3rd street promenade.
Also worth a visit is the Huntington Library and Gardens in San Marino (12 miles from Los Angeles), as well as a few beaches along the coast, especially Malibu.
Finally, Warner Brothers Studio gives out free tickets for people to be in their live studio audience.
Sorry for the long post. Only reason I know about all this is that I'm from LA.
Tons of places at all these high-ranking unis