I live in Minnesota in a suburb of Minneapolis. I haven't done too much south of the Twin Cities but if you have the time to drive north, the Superior Hiking Trail is absolutely fantastic. I plan to put a trip report with pictures and the obligatory hammock photos soon. I've never been to the Appalachian Trail but I'm suspect that I am spoiled for all other trails after this one. We did 30 miles in 4 days and we went from one stunning vista to the next. I took a swim in a waterfall. There is one campsite right on another waterfall. In some places we were 500 feet above the forest floor with a full view of mountain lakes and trees. It is going to be insanely beautiful once the leaves turn.
Other than that, I've been to state parks near the Twin Cities and in Wisconsin. Lake Maria Park (MN), Sand Dunes National Forest (MN), and Levis Mound (WI) are very cool places. Lake Maria is a state park with dedicated hike-in campsites about 1/3 to 1 mile from the parking lot. They are fairly isolated from each other with no shortage of trees. Sand Dunes Forest is being logged and is not quite so nice but since you can camp anywhere you like. You don't need to be at a campsite in MN state forests.
Here are some good links that may help.
Levis Mound is primarily a mountain biking trail but I did an adventure race there and the geography is pretty interesting.