Washington, District of Columbia - Never
If DC had been given electoral votes after the Civil War, I kind of wonder when it could have gone Republican, if ever.
1924 and 1928 are definitely possible, but I think it would have swung hard against Hoover in 1932 because of his response to the Bonus Army March.
For whatever reason, the whole DC metro area swung hard towards Dewey in 1944 and 1948, so I'm not ruling out a win in either of those years, especially the latter.
Ike won Baltimore City in 1956, so he conceivably could have won DC as well. That's the absolute latest it could have possibly happened.