William Henry Harrison died on his 32nd day as President, so old Tippecanoe didn't have much chance to cause trouble. He is considered among the greats for that reason alone.
John Tyler, Harrison's Vice President was his successor. He was also one of the greatest because he was in the Whig Party and fooled all those evil Whigs by being a strict constructionist Jeffersonian.
DiLorenzo explains it all here:
The President Who Was Expelled from His Own Party
(And the First to be Subjected to Impeachment)
https://www.lewrockwell.com/2020/02/thomas-dilorenzo/the-president-who-was-expelled-from-his-own-party/
Spey asks Question #1: "Was there any president you have liked during your lifetime?"
I did like Reagan's anti-left rhetoric. A mixed bag on policy.
Trump was at least amusing, but again a mixed bag on policy.
Spey's Question #2: Is there any president throughout our history you have liked?
It's a short list. The last president I would have wholeheartedly supported if I were alive back then was Grover Cleveland.
More recent than that, Coolidge was good.
Aside from Harrison and Tyler already mentioned, Jefferson was cool and certainly important as an indispensable man like Washington and Madison, but like others he was best as not-president than the president. 1st term good, overthrowing the the terrible Federalists (misnamed, actually nationalists), the second term not as good.
Martin Van Buren was a great one, a Jeffersonian to the core, one of the true "Old Republicans".