My husband and I really liked LACMA. It has a very impressive permanent collection (from American greats, Mary Cassatt, Alfred Stieglitz, and Richard Diebenkorn, to Europe's finest, like Henry Matisse and Rene Magritte). We also enjoyed the Images of Fashion exhibit, with rare fashion engravings from the Louis XIV era.
Our kids loved the tar pits, which are eerie but fun.