I checked Jefferson, Johnson and Nixon. With a bit of help from Wikpedia, here are my reasons:
Jefferson because, well, he was just so all-around brilliant. Anyone who has ever visited Monticello can't help but emerge amazed. He was a skilled writer, horticulturist, diplomat, university founder, vicarious explorer (Lewis & Clark), inventor, philosopher, architect and, oh yeah, president. But of course, he was far from perfect. He was outspoken in his belief that slavery was immoral, and yet he owned slaves. He promised to free his slaves when he became debt-free, and he never did. He wrote about slavery, "We have the wolf by the ears; and we can neither hold him, nor safely let him go."
Johnson and Nixon are almost like bookends -- complex, multifaceted men with outsized personalities. Both had the capacity and desire to do good, both were marred by Shakespearean flaws. By pushing through the Civil Rights Act, the Voting Rights Act and the War on Poverty, Johnson did more good than I think any other president has in recent years, but then came Vietnam, his undoing. Nixon did more evil than any president in recent years up until (and, some might argue, including) the incumbent. But he did some good things, too: Created Head Start, the EPA, OSHA, and the first federal affirmative-action program. He wanted to create a universal health-care program (but didn't succeed). He traveled to China and engaged in direct talks with leader Mao Zedong, established détente with the Soviet Union. But then the dark side -- he was haunted by paranoia and insecurity, bombed Cambodia, engaged in illegal acts and coverup in Watergate.