I don't think you'd see too many people disagree that Jefferson was the smartest man to serve as president. Garfield, Kennedy, and Clinton were also brilliant, and honestly, we've had few (if any) truly unintelligent presidents.
Jefferson was a genius as an architect and as a writer (his personal letters comprise one of the great achievements of American literature). He made the right decisions as President on the Louisiana Purchase, the Bill of Rights and the founding of West Point (so he was truly a great pres). But in some other ways he wasn't so smart and didn't have good judgement. Apart from his knee-jerk views on black folks and on slavery, he had a fatuous naivete about the Jacobins who highjacked the French Revolution--and his vision of an agrarian America and his dislike of commerce and industry were likewise kind of, er, limited.
Presidents with the best judgment: I'd say Washington, Polk, FDR, Truman, Eisenhower. Not Lincoln; although a great President, he made too many mistakes, especially in dealing with his military commanders. Smartest presidents: Jefferson, Madison, Lincoln, Eisenhower, TR. People forget that Ike was one of the U.S. Army's top intellectuals (military intellectual, not in other respects) before WW II, and that he was better educated than most presidents thanks to Fox Conner and the Army Staff College. And there's a reason Crusade in Europe is just about the most quoted book about the war against Hitler.
Re Clinton, I'm not convinced he's all that bright except in emotional IQ. As to Kennedy, if he really wrote Why England Slept he was smart as hell--but I don't think he wrote it, and nothing in his life thereafter would suggest he was the kind of intellectual who could produce a book as brilliant as that. His daddy made him president.
So it comes down to Ike who best blends smarts with judgement. If I'm wrong about Lincoln's judgement, and some people would think I am, then you have Ike and Lincoln. But if you throw the third element into the hopper, emotional balance, then you're left with Ike. The type of crisis that he would have been best at handling, however, never came along in the 1950s, and for that we can be grateful since it probably would have involved a horrific showdown with the Soviets.
Ike got to be the right man at the right time in the right place ONCE in his life. And once is enough for anyone. Or maybe the fact that there WAS no crisis in the 1950s suggests that he indeed did it twice. Sometimes greatness comes from maneuvering to avoid crises rather than dealing with them after they've metastasized, and thus the leader's role becomes almost invisible to historians.