The California Science Center has free admission to the permanent galleries. This could take a long day in and of itself. They also have an IMAX there, if you want to splurge.
Do you have any zoo or museum memberships? Often, they "transfer" to other places, and other places give deep discounts. For example, I looked at the Phoenix Zoo and you get reduced admission at the LA Zoo, free admission to the Cabrillo Aquarium, etc.
There's a neat Children's museum, but I don't know about the cost.
I'd spend at least a half day roaming around Hollywood walk of fame/Chinese theatre. Up on the second floor of the Roosevelt Hotel there's a really cool pictoral history of Hollywood that few except for the locals know of. You could go to the Disney soda shoppe for a treat while there.
Not sure when you're planning to go, but if it will be warm, maybe go to more than one beach. Honestly, the kids may have a great time just hanging by the pool for the bulk of a day if it's warm enough.
You could drive out to Palm Springs. There are pretty cool things to do out there, including a fairly inexpensive children's museum and the Living Desert. If you're going to be there between Thanksgiving and x-mas, the living desert does a walk the wild light activity that is fairly inexpensive (I think like $5 per person) and its just beautiful. Also, in the Torrance area, they have a beautiful neighborhood where everyone in the neighborhood puts up white twinkle lights in their trees for blocks on end and all the houses try to outdo each other with x-mas decorations.
Take advantage of kids eat free and or free admission days if you can.
I found a book at barnes and noble called "Free L. A.: The Ultimate Free Fun Guide to the City of Angels" It sounds great!
There are some great libraries around that would be free. A number of the area shopping malls have ice skating. Maybe bowling. These are types of things you can do at home, but if you are looking for fillers, these might be good stand-bys.