From John Hennessy:

President McKinley in Fredericksburg in May 1900. He is in the carriage, his face toward the camera. Click to enlarge.
Years ago I did a program at the Fredericksburg Area Museum called Footfalls of the Presidents, an offshoot of their Footfalls of the Famous exhibit on notable visitors to Fredericksburg. The program chronicled the visits of sitting, future, and former presidents to our area. Some visits were incredibly brief (the record for shortness stands at three minutes), others mundane, and some were emphatically important. At least two presidential trips to Fredericksburg involved real or threatened violence, including the first physical assault ever made on a sitting president (Andrew Jackson, though the assault took place during his travel to Fredericksburg). One president (Monroe) lived in town for several years. Some stopped as a matter of convenience on their way through; others came for momentous reasons.

Judge and historian John T. Goolrick greets President Harding at the 1921 Marine Corps exercises on the Wilderness Battlefield. It was Goolrick, incidentally, who in 1924 would urge the removal of the slave block in downtown Fredericksburg, arguing that it had never been used to sell slaves.
By my count, 31 Presidents have visited the Fredericksburg region at some point in their lives–thirteen of them as sitting presidents.
The list as it stands today is below–given in order of their presidency, not necessarily in the order of their visits.
The question is, does anyone know of any more?
Here is the current list:
Washington
Jefferson
Madison
Monroe
Andrew Jackson
Van Buren
John Tyler (Tyler and Harrison visited together on their way to DC for the inauguration in 1841)
W.H. Harrison
Polk
Taylor
Fillmore
Lincoln (May 23, 1862–see here for more)
Jefferson Davis (March 22, 1862, stayed at the Doswell house on Princess Anne Street)
Andrew Johnson (perhaps the shortest visit–he refused to come off the train)
Grant (never here as president, but in Spotsylvania extensively in 1864)
Chester Arthur (married Ellen Herndon, whose extended family lived in Fredericksburg; she lived here for several years as a child)
Grover Cleveland (dedicated the Mary Washington monument in 1894)
McKinley (here for the meeting of the Society of the Army of the Potomac in 1900)
Teddy Roosevelt (whistle stop)
Taft (whistle stop)
Wilson (in Milford, Caroline County, and almost certainly in Fredericksburg)
Harding (attended military exercises at Ellwood in 1921)
Coolidge (dedicated the new National Military Park in 1928)
F.D. Roosevelt (twice, perhaps three times)
Eisenhower (speech at Mary Washington monument in 1954)
Bush41 (a memorable visit to Goolrick’s)
Clinton (campaign)
Bush43 (South Stafford)
Obama (campaign stop)
Donald Trump (campaign stop)
Biden (wedding at home on Indian Point)