The Treaty Room—filled with memorabilia including one of the President’s two Grammy Awards, family photos, and a personalized football—is where Mr. Obama often retreats late at night. He uses the room’s namesake table (far right), which has been in the White House since 1869, as a desk. George Catlin scenes of Native American life hang on walls covered in custom-stenciled Larsen abaca. Eighteen-fifties overmantel mirror; 1930s Hereke carpet.