There was one once upon a time. It was called
Musée du Cinema in Paris, France. It was created by Henri Langlois, who was co-founder of the Cinémathèque Française. Mr. Langlois was a cinemaphile, a pioneer in film preservation and film history. Many people know of the Cinémathèque Française, as it started the French New Wave.
From what I remember of the documentary,
Henri Langlois: The Phantom of the Cinémathèque, a lot of filmmakers sent items to Mr. Langlois, resulting in a collection of more than 5,000 movie-related objects.
Unfortunately, the museum burnt down in July 22, 1997 (while it was locked in the middle of a court case between the Government and the Cinémathèque Française). I don't know if any or if all of those items were destroyed by the fire or survived.
But to make a long story short, there was a place once upon a time. Now, there's more of smaller dedicated places that are more themed, like the Judy Garland Museum or the motion picture corner of the Smithsonian's Museum of History and Technology.