John, there is a lot of things to do and see in L.A. I would say it is dependent on your transfer to LAX and if your ship ports in Long Beach or San Pedro. Both have close by attractions. Long Beach has the Queen Marry, Shoreline Village and the Aquarium of the Pacific. San Pedro has Whale watching and harbor tours. San Pedro used to have Ports Of Call village but it is being torn down.
L.A. has everything from Rodeo Drive, Beverly Hills, Hollywood Blvd walk of fame to world class Museums Like Museum Of Contemporary Art MOCA at the La Brea Tar Pits, the Peterson Automotive Museum, Santa Monica 3rd Street Promenade and the Pier, Venice Beach and it is not LA LA land without all the Studio tours or Tour of famous peoples homes.
The Issue will be luggage, time and $$$. The Ship web site is only offering 2 excursions in LA (It is a shame they do not offer a good city tour of L.A). Santa Monica & Venice beach, 5 hours (they are next to each other) or Universal Studios tour an Amusement Park, 7 hours where 2 hours or more will be in the buss. If you choose Universal Studios, yell me a "Hello", I live a few miles away. If it was me out of the two I'd do the Beach Cities excursion to fill the day.
P.S. If you look up transportation from Long Beach to LAX, The Subway does do it with the Blue line to the Green line and then a Taxi to LAX. The Blue line is being remolded, not sure if it will be done by time you are here (they are running a buss where the train is not running, so it takes much longer) Also Those lines run through some not so safe areas. My old coworker that used to take the Blue Line from Long Beach to Down Town L.A would carry a knife in her bag for protection.