There are quite a few in the area. Have you tried Travelocity (www.travelocity.com) to see what's available?
One I've stayed at several times is the Hacienda Hotel at www.haciendahotel.com, and it's OK, not my favorite because you have to check in before 4pm to get a choice of rooms. Otherwise, the rooms are nice.
Actually, I found a good deal ( I think).Its called Fly and Cruise. It is designed for the passenger who is arriving in LA by air. They pick you up at the airport, take you to the hotel, and transfer to World Cruise Center the next am. If you need more info. E-Mail me.Oh, and of course accommodations for the night are included.
Check out the Crown Plaza LAX Airport. On my return travels from my last cruise, I got a 21-day advance purchase rate of $59 for one night (which happened to be a Saturday night). The only caveats on this rate are that you must pay in full at least 21 days in advance and it's non-changeable and non-refundable if you don't go.