First of all, welcome to LA.

If you are landing at 10pm and you are jet lagged from Australia, why not just go to the Beverly Hilton or another hotel away from the airport. That way you do not have to unpack for one night and the $$ difference is not that substantial.

I would definitely rent a car. Public transportation in LA is terrible. If you are nervous about driving on the right side of the road, I understand. But I have driven on the left side of the road many times and while not easy, you just need to maintain focus.

There are many other threads and blogs about LA with kids, but aside from Disneyland, I would recommend the rides on the Santa Monica pier as well as a drive to Leo Carrillo State Park in Malibu. The only suggestion is to get there early, especially on the weekends. The same holds true for Disneyland. Do NOT go there on a weekend.

If you want to go to a Lakers game, check their schedule on http://www.nba.com/lakers/schedule/index.html You can go to ticketmaster.com and get tickets and sometimes if you look a few days before the game, some better seats open up. If not, check ebay or stubhub.com for seats. If you can afford it, avoid the 300's and get seats in the 100's, 200's or premier seats.