If we're going to divide Presidents by era, I'd have to say Eisenhower for the 20th century and Grant for the 19th. Washington for the 18th century (no competition there). I'd also add Washington to my list of all time greatest persons who happened to become President. I don't think we should include Presidents who are still living, because we really don't know what they might achieve in the years ahead (Clinton and/or Bush II may do something really extraordinary before they die).
So to divide things up a bit more, let's have greatest President (as a non-President) among those who served as President during:
18th C - Washington
First half 19th C - J.Q. Adams
Second half 19th C - Grant
First half 20th C - TR
Second half 20th C (living ex-presidents excluded) - Eisenhower
This of course would include their non-Presidential achievements that occurred in the half century preceding or following the half-century in which their occupation of the White House occurred.
And I'd like to add a list of Presidents according to their contributions to American literature:
1. Jefferson (Decl. of Independence plus his voluminous personal letters)
2. Grant (he'd be first except that he only wrote one book)
3. John Adams (for his letters)
4. TR
5. Eisenhower
6. Madison (I think the Federalist Papers qualify as literature)
7. Jimmy Carter (a surprisingly good poet; also wrote a historical novel that wasn't panned--is he the only President who ever wrote a novel?)
I don't include Lincoln because his literary achievements as a speech writer and author of state documents were made while he was serving in the White House for the most part. If he'd survived to write his memoirs he would probably be in the top three.