Based on looking at 2008 and 2012 city and county results, I've come up with this. Gray states are uncertain.
Any particular reason why Jefferson City, Missouri is so right-wing?
I have no clue why Jefferson City is even the capital of Missouri. It should be St. Louis. Jefferson City has like what, 10,000 people?
Probably because it's near the center of the state. It's why the capital of Pennsylvania was moved from to Harrisburg.
Of course, Columbia is a much larger Obama-voting city also near the center of the state. I suspect there's some historical reason that doesn't have much meaning now, but moving the capital isn't worth the hassle. Same with Kentucky where now Lexington would be a more logical capital than Frankfort, but it's not that big of a deal.
Jefferson City does have over 40,000 people and is much bigger than it's being described though.