I checked very briefly on Google and noticed one San Pedro hotel lists the taxi cost as $40 (one way), time about 30 minutes - from my observation, that would be in very good (light) traffic. Time more likely should be 45 minutes. If you type in "taxi service LAX to San Pedro" you might be able to pick up more detailed information. Which cruise are you on - and when?
Get the cruise transfers it is much cheaper. WE paid $38 r/t each. The traffic is terrible, very heavy even on a Sunday evening.
It is a 40-45 minute ride.