My family and I have hiked the trails of Afton State Park many times over the years. It is best in the Fall, when the leaves are turning and it is not too hot, but also enjoyable in the Spring (although a bit muddy in places), the Summer (bring water to keep hydrated), and even the Winter (intended for cross country skiing at that point). Most people head North - to the left of the parking area - but I recommend heading South (to the right). You will come upon a plateau of Prairie flowers, a winding path, a descent into the woods, a very steep, rocky path down to the river (sometimes we have stopped for a picnic halfway down), then a lovely walk along the St. Croix River on what was once a railroad line. One day there were people mushrooming, and there are always people with kids and dogs enjoying the walk, with a breeze off of the river. The boats (and their motors) on the river don't create too much noise. Eventually you come to a beach, and then it is time to choose which path back up the hill - and having hiked quite a distance, this is the hard part - but it is exhilirating.
Leaving the park you wind your way out on a narrow road, slowly, with a sense of calm.