The Natural History Museum is across the street from USC. In fact, you should visit USC, too, although I probably won't be there much during the summer.
Definitely make sure you go up to the Griffith Observatory! Parking and entrance are free, and you get a beautiful view of the city (or the smog).
Will Rogers State Park is a neat place, too. Will Rogers' mansion is there, plus a lot of open space and some horses. They host polo games every Saturday and Sunday.
As for beaches: Most beaches near LA are sandy; some rocky beaches are found further south. Santa Monica is a popular beach; I don't really like it. Venice beach is a place you should go once, just to see how crazy it is. Manhattan beach is a bit more low-key (but the one day I was there it was raining, which will make any beach less busy).
I also checked out Abalone Cove, which is a rocky beach in Palos Verdes...got there at the end of the day, and there were only a few other people there. The parking lot closes at 4:30 (they let you stay later, unofficially, but they don't let you in after that).