The La Brea Tar Pits, the Getty Center, the Museum of Natural History, the L.A. Zoo, the Aquarium of the Pacific (in Long Beach), the Queen Mary (also in Long Beach).

If you're going to be near Disneyland, you're actually going to be in or near Anaheim, which is in Orange County. Orange County is on the ocean, so there's lots of beaches (not in Anaheim itself, but not terribly far, either, and the weather may be nice; it's hard to predict in early December). Anaheim is also home to Angels Stadium. Disneyland itself is fun, and there's also the California Adventure theme park.

There's a Metrolink station in Anaheim that can take you into various parts of the L.A. area.

"Oh, you can’t help that," said the Cat: "we’re all mad here. I’m mad. You’re mad."
"How do you know I’m mad?" said Alice.
"You must be," said the Cat, "or you wouldn’t have come here.”

- Lewis Carroll, Alice in Wonderland