7 Answers

For me it,s the Tate Modern, London.

If you are in the USA the Chicago Museum of Art is recommended.

The Metropolitan Art Museum in New York  would be my first choice.

Museum of art in Washington, DC. Mind blowing.

I travel often for work and make a point of visiting museums in the cities I stay in. Most major urban centers have decent museums. The Art Institute of Chicago is very impressive, in fact Chicago is a great town for museums period. It also depends on what you want to see. The San Fransisco art museum has Kienholz tableaux which are rare, and Houston has the Surrealist museum as well as the Rothko chapel. New Orleans has the Ogden which displays a terrific outsider art collection and St Petersburg Fla (if I remember correctly) is home to the Salvador Dali Museum which is a feast for the psyche if that's your thing. Wow, now that I'm thinking about it I'd love to go on a national museum visiting vacation. That's something worth getting a piggy bank for. 

The DIA- - - Detroit Institute of Arts is one of the finest art museums in the world.They have many originals. They have quite a diverse array of amazing arts. The Diego Mural is spectacular  

And they have the finest collection of Irish gold, but they keep it under lock and key. 

The Art Institute of Chicago is awesome, but if you really want an art hub, go to NYC. You can hit the Met, the Museum of Modern Art and the Guggenheim - three spectacular museums that are all found in the city.