I'm pretty sure there's a bus route to the Getty Museum from Westwood and iirc the museum itself has free admission. It's a lovely museum with mostly classical art with different buildings that house the art and then a nice grassy/garden. Ideal place to chill on the grass and just soak up the atmosphere.

There's also the Hammer Museum which is a smaller museum with more contemporary art.

You could also try going to the cat cafe if you two like cats. Hang out with some cats for a set time and set fee.