Los Angeles started developing rapidly at the turn of the century. In 1920s, it had 80% of global film production, and the world’s highest concentration of movie theaters in its Downtown district. While the golden age of movie palaces is long gone, and many of the theaters closed down or were re-purposed, their architecture is still there to admire, so why not have a look.
Also, the ever-essential Wikipedia has an abundance of information about Downtown LA, the Broadway, the Theater District, and on particular theaters — the Los Angeles, the Mayan, the Metropolitan, the Million Dollar, the Orpheum, the Palladium, the Tower and the United Artists — as well as other buildings: the Broadway Arcade, the Bradbury, the City Hall, the Eastern Columbia and the Union Station.
Note I use the theater spelling here for consistency but some venues actually spell their names with an -re. Also note that not all these buildings are examples of Art Déco architecture, other styles include for example Gothic Revival.