Without a doubt, the Getty Museum is one of the places every visitor to Los Angeles should see.
Jean Paul Getty (1892 - 1976) was an American who made his money by founding the Getty Oil Company. A collector of art and other antiquities, when he died his money went into the J. Paul Getty Trust, which funds and operates the Getty Museum. The museum is a part of the larger Getty Center, which operates a research institute, conservation institute, grant program, and leadership institute.
The museum contains classical:
manuscripts
furniture
art
in addition to being flanked by a 134,000 sq. ft. garden
There are many more sights to see there, but you know they did things right when half your pictures turn out to be just of the building itself.
Oh, and best of all, entrance to the museum is free -- you only have to pay for parking.