This Saturday, September 28, 2013, is Museum Day, when hundreds of museums across the U.S. offer free admission.
Participation is limited to two tickets per household, and must be ordered online in advance (I think you can order on Saturday before you go).
Search for participating museums near you by address or by state.
The event is coordinated by Smithsonian magazine.
(Images above, a few museums I like to visit in Delaware: Delaware Art Museum; Pennsylvania: Brandywine River Museum, Rosenbach Museum; and New Jersey: Newark Museum, Montclair Art Museum)