I've been to the Louvre, the Met, the National Gallery in London, and the Cleveland Museum of Art still gets great marks from me. The open galleries are quiet and inviting--no massive throngs to fight , or shouts from unappreciative patrons. The collections are varied and beautiful, and hold many gems from Matisse, Picasso, Monet, and more. New galleries are opening all through 2013, and the addition of a great restaurant and lots of seating make the museum a great place to spend an afternoon.
Best of all? It's completely free. I love you, Museum of Art!