If you’re into art and old stuff, run 10 minutes north on the 405 to the Getty Museum.
The Getty is wonderful — especially on a clear day. Excellent suggestion.
There’s also the Norton Simon in Pasadena. You can take I-10 to the 110 which will take you all the way to Pasadena. This trip has the added advantage of letting you experience the Pasadena Freeway, Southern California’s most exciting roller-coaster!
The Getty Museum is closed on Monday - which is the day I have the most time and the other days I don’t get out of testing sessions until just minutes before it closes. What a shame as I would really liked to have seen it.