Right across the border from Minnesota into South Dakota is a charming state park called Palisades. Definitely worth a visit on your way to the western portion of the state.
Mike and I really enjoyed our morning hike traversing most of the park. The trails are of moderate difficulty, with some hopping from rock to rock, small hills, interesting landscapes and beautiful views. Oh, and a pack of wild turkeys (the mystery birds from the other night revealed themselves to us while we were hiking).