Completed in 1881 just in time to host President James Garfield’s inaugural ball, this redbrick and sandstone structure was the first Smithsonian museum on the Mall, and the first U.S. National Museum. But despite the near completion of a decade-long renovation, the building remains mostly closed to the public except for special events and exhibitions. You can always admire the building’s exterior. Weather permitting, a 19th-century carousel operates across the street on the Mall.