According to Eat This, Not That Website, the best 24/7 restaurant in the Land of Ten Thousand Lakes is located in the far southwestern part of the state, in the small town of Pipestone.
Some of the best restaurants around are the hole-in-the-wall ones that gain their reputation by word of mouth. Minnesota is full of these, but the very best is nestled in the southwest corner of the state, and there's a good chance you've never heard of it.