The concept of museums dates to 2500 years ago when a Babylonian prince felt the necessity of presenting art to the public and preserving artifacts for future generations.
The Capitoline Museum in Rome is the oldest in the world, within walking distance of the Colosseum, and established in 1471 under the observation of Pope Sixtus IV, who donated many artworks and sculptures to the museum. It was opened to the public in 1734.
Click on the blue link and read about the 10 oldest museums. My preference is for religious art to be in churches because museums are a little bit dead.