Ah, a question I can finally answer!

The short answer is: it never left Washington D.C. According to journalist and author Garrett Graff, who's book "Raven Rock: The Story of The US Government's Plan to Save Itself- While The Rest of Us Die," is a pretty complete picture of current Continuity of Government plans, and a history thereof; the nuclear football stayed behind at The White House, despite the fact that President Nixon would still be president for another two hours after boarding Marine One and subsequently Air Force One. While the call sign of Air Force One changed to SAM 27000 mid flight, the nuclear football was next to the incoming president and not the outgoing president.

Even more significant, though, is what then-Defense Secretary James Schlesinger recalled years later. Namely, that members of the National Command Authority (NCA), including Kissinger and the SecDef, were so concerned about Nixon's behavior and heavy drinking during the last few weeks of his presidency, that he issued an unprecedented and, probably illegal, order: if the President issued any nuclear launch order, the people responsible for carrying the order out were to first check with Schlesinger or Kissinger before proceeding.

"Nixon himself had stoked official fears during a meeting with congressmen during which he reportedly said, “I can go in my office and pick up a telephone, and in 25 minutes, millions of people will be dead.” Senator Alan Cranston had phoned Schlesinger, warning about “the need for keeping a berserk president from plunging us into a holocaust," writes Graff.