I need to stay overnight at LA Airport in December with wife and 2 children 9 & 12. Any suggestions

Take a hotel on Century Blvd, all with airporthsuttles, like Crown Plaza, Sheraton, Holiday Inn, Radisson etc.
In front of the hotel there is a free shuttle "tram", 1 x per hour to Manhattan Beach, pier and small shopping Mall.

I'll be staying at Courtyard LAX next week. The price is roughly $200.

Hi Petersfamily

Check out Embassy Suites Embassy Suites LAX North
I was just down there, includes full breakfast Lots of room

Have Fun
GP

Four Points Sheraton LAX is recently renovated and the shuttle service is good.

If it's a weekend night, or holiday period, hotwire and priceline usually have the airport hotels deeply discounted. I've seen the Hilton and the Westin come in at around $60 to $80, consistently. I wouldn't book a budget hotel this way because some of the budget places near the airport (3 stars or less) can be in undesirable areas. But the four star places are all well located. Don't book too early as these deals are non-refundable, but you can start checking prices now to get an idea.

I agree with Embassy Suites or the try the Doubletree.