Location: New York
2013 Exhibitions: Walking Drifting Dragging (January 9 - February 3), NYC 1993: Experimental Jet Set, Trash and No Star (January 16 - April 21)
Since 1977, the New Museum has been Manhattan's only museum dedicated exclusively to international contemporary art. They've introduced exhibitions of artists such as Ana Mendieta, Christian Boltanski, and David Wojnarowicz, anticipating their later, world-wide recognition. You'll still see big names included in their small collection, but also be prepared to encounter artists who are completely new and need to be on your radar. Their rooftop also has stunning views of downtown and midtown Manhattan.