Downtown L.A., Pershing Square, MOCA (museum), Bunker Hill steps (633 W. 5th Street), Disney Concert Hall, Little Tokyo, Olvera Street (Historical Mexican street)
Check out http://www.downtownla.com
West side:
Santa Monica Pier (Kid will love the sand), 3rd street promenade (Santa Monica), Henessy Ingalls bookstore (on Wilshire in Santa Monica), take a drive along Pacific Coast Hwy. to Malibu., Venice Beach, Getty Museum (on Pacific Coast Hwy, and the new one in Brentwood.
And many many more….enjoy…..