First of all, you will be cruising out of the port of Los Angeles, not Long Beach, the port of Los Angeles is in San Pedro and about a 20 minute drive by taxi from the Long Beach airport. I always recommend no one book a flight before noon on debarkation day. I can't imagine you will have any problems. NO, no not do Orange County, it is a much longer drive...Long Beach is a small and very managable airport..
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