Pooch,
I am another lifelong native. If you are wanting to take the light rail from LAX, you will have to take the bus to the Aviation station, go upstairs to the Green Line, then connect to the Blue Line to get to downtown LB.
I enjoy taking the Blue Line up to the Red Line (subway in downtown LA) where you can go to either Hollywood or connect to the Orange line at Union Station and go into Old Pasadena where they hold the Rose Parade. It is a great way to spend a weekend day.
I agree the better beaches are south in Seal and Huntington Beaches which by the way have great little communities. Go see the QM and the aquarium. You will have great weather and if you come during the right time of year, you can go surfing and snow skiing on the same day.
Enjoy, Dave