From LAX to just about anywhere in San Pedro two choices. Shuttle, there are several, we prefer Super Shuttle, the blue van, and for just about any of them it will be around $35 plus tip for two of you. Other option is a taxi which if I remember but it was a while ago, around $50+ plus tip but this may have gone up since it has been a while since we have taken a cab.
There are several choices in the area as far as hotels, we always stay at the Vagabond, it is right on Gaffey so it can be a little noisy but it is simple, clean and around $100 sometimes less if you book online and you can actually see the top of the ship from the second and third floor. They have a free shuttle to the port which is only a 5 minute drive, it takes longer to load and unload the shuttle then the trip and the driver uses a back gate so you miss all the crowds at the front gate. Several fast foods close by plus a sushi restaurant right on the corner plus just a short cab ride to ports of call for some higher end eats...