LAX to port terminal is quite a long distance. Suggest you take the cruise bus from LAX to Port Terminal which is located in Long Beach, or take the Super Shuttle. A cab will cost the most and the freeways are very crowded as the meter runs in heavy slow LA traffic. Suggest that you call your travel agent, arrange bus pick up from LAX to Long Beach......
Otherwise be prepared to pay big bucks each way.
Sorry for any confusion....I consider Long Beach and San Pedro one of the same. San Pedro is the name of the city, while the ship is directly docked across from the Long Beach shipyards.
San Pedro is the offcial sailing dock.