Come to Vegas for 2 of the 4 days!!! it's not that far..
As for LA.. Venice Beach is always good for some fun..
West Hollywood is very chic and gay but great shops and cafes
Go to a taping of a TV Show.
Here is a link for ordering tickets.
This one also has some of the gameshow links as well.
Getty Museum is good -- They have nice gardens.
1 day trip via boat to Catalina with lunch?
Come to Vegas for 2 days.. :-)