I am not quite sure what " went for" means to you. Only two presidents announced early in their administration that they would not seek a second term and they were James Polk and Rutherford Hayes.
Barack Obama is the only Columbia alumnus.
I can only think of one and that was Woodrow Wilson.Several other presidents went to school in states that were future Confederate state or had been confederate states when they lived there.
No US presidents ever went to Syracuse U.
One. Gerald Ford was a U. of M graduate.
There were several presidents that went to Nelson Mandela's funeral. President Obama from the US attended.
Only Jefferson went by Thomas. Woodrow was given the first name Thomas but started going by his middle name when he was a young man.
Chester A. Arthur; Jimmy Carter did graduate work in reactor technology and nuclear physics; William McKinley attended Albany Law School which is a part of Union University, which is now a consortium between The University at Albany (SUNY) and Union College, but was not when McKinley went there.
Obama went to Canada.
JFK went to Choate
George HW Bush
U. S. Grant, Dwight Eisenhower and Jimmy Carter were the only US presidents who went to military schools. All of the other 40 did not go to milatary schools. See the related question for their names.
Jimmy Carter, George H. W. Bush, Bill Clinton & George W. Bush