As a native Angeleno, I would suggest a stay at a LAX airport if you have an early morning flight the next day. We did this right after our wedding in 1995, staying at the Marriott that night, and catching the hotel shuttle to the airport for our morning flight to Honolulu.
The downside to staying here otherwise is that you are not near too many restaurants and it's not a great place just to be walking around. To get anywhere for a bite to eat or a store to buy the things you forgot, would take a taxi, which are expensive here.
Many people who are coming in for a cruise from either San Pedro (most of the cruiselines) or Long Beach (Carnival) find it better to stay in San Pedro, Long Beach, Santa Monica, or other beach cities. SM's hotels may be a bit costier, but I find the Third Street Promenade nearby to be a nice place to eat (lots of restaurants, stores, street performers). It's an pedestrian only outdoor mall that's just a few blocks away from Ocean Avenue.
Long Beach is a short taxi or shuttle ride away from San Pedro and has some nice restaurants at Shoreline Village (the Queen Mary and the Carnival berths are right there). You can also enjoy the excellent Aquarium of the Pacific nearby.
San Pedro is basically industrial but many cruise passengers stay in a couple of the hotels there (I think they will shuttle you for free to the World Cruise Center at the Port of Los Angeles.
A major thing to remember is if you get a really low price for a hotel room, beware. The hotel could be located in a bad area.