Bless Roadside America, my first travel-planning stop. Should I try to arrange for a tour of the Bottle Village? Go for the hard-boiled eccentricity of the Museum of Jurrassic Technology? (More coherent review of museum here, on a steampunk blog so you know it has to be good). The Getty Museum and/or Villa and the La Brea Tar Pits are other possibilities.
The Manolo has recommended several restaurants in the area, which I am sure would require me to eat cereal for breakfast and lunch to stay within my per diem: steak, steak, steak, Californian, and the Italian that the Manolo says is simply the best restaurant in town.