Did any presidents live elsewhere during their administrations?

While President George Washington selected the site and approved the design, he never actually lived in the White House— he ended his service as chief executive in 1797 and died in 1799, one year before the seat of the federal government moved from Philadelphia to the city named in his honor. Washington lived in executive residences in New York and Philadelphia, and his successor John Adams also lived at the President’s House in Philadelphia.
While the White House was nearing completion, President Adams temporarily lived at Tunnicliff's City Hotel near the U.S. Capitol. He later moved into the Executive Mansion on November 1, 1800.
After the burning of the White House on August 24, 1814, President James Madison lived at nearby Octagon House for about six months before moving to a private home within the Seven Buildings, another residence not far from the White House.
President James Monroe occupied the Timothy Caldwell House during his tenure as Madison’s secretary of state and then for a short time as president. President Monroe embarked on a grand tour of northern states in June 1817 and then returned to Washington that September. There was a public ceremony to welcome him, and it continued until he arrived at the White House. About a month later, he and his family moved into the White House in October.
In 1902, Theodore Roosevelt used 736 Jackson Place as a temporary Executive Mansion while the White House was under renovation—he and his family also spent some of this time away from Washington at Sagamore Hill, his home in New York. Many renovations or refurbishing projects are purposely planned during the summer months when presidents and their families are away from the White House.
In 1927, President Calvin Coolidge moved to the Patterson Mansion in Dupont Circle while the roof and upper floors of the White House underwent major repairs and renovation.
During the major 1948 renovation of the White House, President Harry S. Truman resided across Pennsylvania Avenue at Blair House, where he lived for about three-and-a-half years. Learn more about the Truman Renovation here.