I would like to visit Minnesota some day....
I've never been. Where should I go and what should I see? I like art museums, bodies of water, nature, peace and quiet with the occasional big city visit. Also scouting out potential cities to move to someday. I'm 50 and don't want to grow old in Los Angeles. I most likely wouldn't be able to handle the Winters there, even though I love cold weather...
Thanks! 
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Drove up I35 to Duluth, always beautiful in the Fall. Duluth for Canal Park and Lake Superior.
Took Hwy 61 North to Grand Marais which is a sleepy art town. You can run around Superior National Forest or view the majesty of Lake Superior and star-gaze.
From there we went to Ely. I don't recommend taking Hwy 1 because it is a 55mph curvy disaster. Ely is a nice old Minnesota town. Anywhere around there you can enhance your enjoyment of fishing or look for a cabin or land for a cabin if you like hunting.
From there we went to International Falls. If you like throwing rocks at Canada you can stay at an old Holiday Inn and throw rocks across the rainy river. I didn't see any Canadians so throwing of the rocks is safe.
From there we went to Eveleth to see the USA Hockey Hall of Fame. Along the way we stopped at a mine where the iron content of the ore was such that you can weld two rocks together. You can also go down in the mine if you like subterranean adventure.
Eveleth, Virginia, Mountain Iron and Hibbing are called the quad cities in Minnesota. You can bounce around there and look at a midwest mining town that surface mines with gigantic mining equipment.
From there our family couldnt take eating out anymore. I would have killed for a home-made salad of some sort.
Nice river towns include Stillwater, Red Wing and Winona. Small towns and lakes abound just about anywhere you go.
Nice hockey tournament towns include Brainerd, Sartell, Saint Cloud and Alexandria. I'd give a shout-out to Wisconsin for cabins but then you'd have to live in Wisconsin. Not cool.
Finally, an old joke for you from a native mud-duck. Q: Why does the Mississippi flow south? A: Iowa Sucks!!! 
One of my most favorite places on earth is Gooseberry Falls State Park, which is about 14 miles or so up the road from the town of Two Harbors, which is up the road (Hwy 61) a piece from Duluth (I can't remember the exact mileage, but it's not all that far).
At Gooseberry, you can park by the visitor center and follow the trail to the falls. If you're feeling ambitious, you can hike along the river all the way down to the shore of Lake Superior. Or, if you want to go directly to the lakeshore, there's a parking area just below it, and you just scoot up a short path and there's the lake. If it's nice weather, bring a picnic - there are all these wonderful old, heavy-hewn wooden picnic tables that were built by the CCC/WPA in the 30s dotted around the upper part of the shore. Or if you want shelter from the elements, there's a gorgeous rustic lodge and picnic shelter built by the CCC/WPA of local stone and timber. (Take a left into a different parking area)
The shore off the first parking area is a gradually sloping mass of folded, cracked, and wrinkled basalt, studded with small bits of crystalline quartz and dotted with tiny pools of water and determined wildflowers. You can hang out and listen to the surf, or set out on the trail that follows the shoreline and winds its way through a grassy upland overlooking the lake, or clamber down the piles of gigantic tumbled boulders that verge the shore below the main trail.
Anyway, it's a wonderful place.
Edited to add:
Photo of the Lady Slipper Lodge on the shore of Lake Superior at Gooseberry Falls State Park.
