LAX does not have a train to city center (they aim to get one done by the Olympics). It does have busses to Culver City / Santa Monica, although the busses stop

LAX does not have a train to city center (they aim to get one done by the Olympics). It does have busses to Culver City / Santa Monica, although the busses stop fairly far from the terminal and you need to transfer to a second bus to get to the terminal. You can somewhat mitigate this with the "flyaway" bus. So, for instance, if I was in Koreatown I'd get the subway east to downtown and get the flyaway bus to LAX. If I were in Gramercy Park, I'd have to take 3 busses. When I lived in Culver City, I could get the Culver City 6 to almost to LAX and then had to walk or use a shuttle to get to the terminal. If I was in Brentwood, I'd have to get a bus to somewhere near Culver City, take the 6, then walk or use a shuttle to get to the terminal. I'm not really sure what you'd call "city center" for a city like LA, but no matter where you are, there is absolutely positively not convenient transit to get you from there to LAX.