Any of the little parks in Santa Monica near the water are good - you all could run around on the grass for awhile, then grab lunch on the promenade, stop in one of the shops that has activities for kids - face painting, paint a clay sculpture, etc.
Best beaches for actually going in the water - probably Segundo - you need to drive south along the south, about half way to OC. Beaches for viewing, lounging and side activities like biking, eating in the sand - start out in Marina Del Rey, rent some bikes, and head north to Santa Monica. You can start out with a late breakfast in Marina at one of the cafes on Washington Blvd and get your bikes after.
Obviously, Disneyland is a fun day trip. Other stuff in LA proper - the Getty has a thorough section for children, Alvera street in down town - not a full day of activities though so you may want to pair this with a visit to China Town which is not too far from Alvera. Those are friendly for the whole family, but obviously there are kid-specific things too.