I can't speak to the food aspect of this post as I'm sadly unfamiliar with good LA Eats but I'm totally team Huntington and Getty Villa! Though I'm also team Disneyland... But seriously those locales are so beautiful. I love the idea of the Getty Villa because it is a really neat way to enjoy Malibu, which is a beautiful but mostly residential city. It is also a great way to travel through LA (though not necessarily faster).
I want to make sure you recognize too, as someone above quoted, that June in CA is known to be our gloomiest month. Beaches are rarely warm and sunny in June. They're still nice! And they aren't super cold. There's just a marine layer that might last most of the day, the morning for sure, and won't fit the image of a a sunny beach vacay.
There's really SO much to do on a California vacation. We can keep suggesting cool stuff to do and amply fill your time!