I go to LA alot on business. Dont move there!
I would recommend Orange County, particularly Newport Beach, Irvine, and San Clemente. In LA county, you can live very well in Pacific Palisades, Malibu, Sherman Oaks, Studio City, and Burbank provided you either earn seven figures or could tolerate a small condo.
I should let you know that I am speaking as a native New Yorker (who's parents are from Newark and Jersey City!) who is now living in the hellhole that is Seattle, but who travels frequently to California on business. All I can say is that if you think life in Jersey is crazy, wait until you spend your first few months in southern California. May I recommend taking a drive on 405 before you decide to move?