These are the main ones in SO CAL there are others mostly private collections.  Jay Leno's comes to mind at the top of my head.

One that I have been meaning to go see is the Petersen Auto museum  http://www.petersen.org/visit/interactive-map   Trip Advisers say it is a 2 hour museum.  Coming the way your are I would take the 405 off of the 5 as you come down the grapevine then take  the 1 east and and after that follow your GBS.  The address is 6060 Wilshire Blvd., Los Angeles, CA 90036. 

Then a little further south is the Marconi museum http://www.marconimuseum.org/

There is a small auto museum which is ok in San Diego Balboa Park.  Now the Park is a great Place.

Here is a picture of the main area http://www.sandiegan.com/san-diego-automotive-museum-balboa-park/