Go to the Huntington Library, the Norton Simon Museum, the Getty, LACMA, UCLA’s Clark Library, the Autry Museum, Walt Disney Hall, the Hollywood Bowl, the Natural History Museum, etc. Go see a play at one of the many live theatres (Ahmanson, Mark Taper Forum, Geffen Playhouse, Pasadena Playhouse, Henry Fonda Theater, Theatre West, etc.).
Go to the beach. Go the Griffith Park. Go to the L.A. Zoo. Go to Busch Gardens, or the L.A. Arboretum in Arcadia.
There are tons of things to do in the L.A. area. The only trouble is you have to drive to most of them.