If you're looking for anywhere that's a close drive away from the Twin Cities, I would recommend checking out some of the Dakota County and Three Rivers Distrct Parks. Lebannon Hills Regional Park is a personal favorite of mine, and a hike around all the lakes within the park will be a solid day hike.
Otherwise, most of the best unpaved trails out there-at least the ones that are upwards to two hours way-are going to be located North of Minnesota. The Lake Superior trail tends to divide itself into multiple pathways allowing you to either take a light easy hike or a more moderately intensive hike.
If you are fine with some smaller trails as well, I would recommend taking some time traveling a bit north of Duluth to take a short walk around Silver Creek Cliff and Fifth Falls located at Goosebury Falls. Both are pretty short hikes, but both are worth the trip! They are not very well known compared to the main waterfall area in Goosebury falls, so they do not get visited by very many people.
A little closer away to the Twin Cities is the Ice Age Trail, in St. Croix Falls. The total trail is 1,200 miles, stretching all the way through Wisconsin. The length of the trail, however, crosses into a lot of popular state parks, so there are segmented trails you can do in a day's hike. If you have time after the hike, I would also recommend checking Taylor's Falls located across the riverside. It's a popular rock climbing spot and has some "Bottomless" potholes that offer an interesting view.
Traveling a little down South East, you can head towards Red Wing and check out Frontenac State Park. This park has two loops on the North and South end of the park. I would recommend getting there early if you want to go to this park, because by mid-day, a lot of people tend to fill up here.
Traveling a little to the South West side, towards Mankato, is a lot of different trails across the Minnesota River. My favorite spot to visit is the Minneopa State Park. The trail crosses the popular Minneopa falls and is also close to the famous Bison Drive Road, where you can take a driving tour to see buffalo(That is, if you are lucky enough to see them out of hiding!). If you have some time, I would also recommend checking out Dairi King, about half an hour away from the park. They have some awesome slushee floats!