West Virginia could give UK some trouble if they can make it a ragged, ugly game. In other words, a typical Bob Huggins coached team game.
Notre Dame, for as good as they are offensively, are just too small. Wichita State, meh.
I think of the teams remaining, these teams would have the best chance. Please note, I'm not saying necessarily that they "will" win, only that they would have the "best chance":
Arizona, Duke, Wisconsin, Louisville.
Why Louisville? Rivalry game and of the biggest proportions at that stage.
Arizona plays such good defense and rebounds so well that it's hard to see either team having anything resembling a comfortable margin throughout the entire game.
Wisconsin is Wisconsin, fundamentally sound, better offense than usual, not quite as good of a defense as usual. Frank Kaminsky really would be the X factor in that game. He's a nightmare matchup for your average big man.
Duke would have to win by outscoring Kentucky, but when they bring their A+ game, no one in the country scores as easily as they do. Jahlil Okafor versus that UK front line would be, literally, epic.
The only other team that I think might have a realistic chance is Michigan State and that is simply because of Tom Izzo. At this point, he needs to just legally change his name to Mr. March Madness. When it comes down to the "one-and-you're done" aspect of the NCAA tournament, I don't believe that anyone is tougher to eliminate than he is. I'm a huge Duke fan (and have zero love for the Spartans) and yes, that last statement includes Mike Krzyzewski. If I needed a coach to win me one single NCAA tournament game, I think Tom Izzo is as good of a choice as anybody alive.