Some thoughts on Minnesota -
If you are in the Cities, the Iron Range is 4 hours away, International Falls is 5 hours away, Grand Marais is 6 hours away. Minnesota is a pretty big State and Minneapolis is the bottom third over in the eastern corner. So plan accordingly as these would be overnight trips, though you might check flights up the International Falls. Maybe you could find a cheap flight and a rental car.
Lake Ithasca is cool in the sense of what you are looking at, but really it is just a lake and you can walk across the river on the rocks. We went, spent hours getting there, then about two hours there including a picnic, then headed home. There's nothing else up there to do....
If you want my advise, concentrate on Lake Superior. Go up to Duluth, get a beer at Grandmas and watch the lift bridge, then head on up to my favorite town, Grand Marais. The drive is incredible right along the shore of Lake Superior. We also get a condo down by the Coast Guard station which gives long views over the water. Eat dinner at the Gun Flint Tavern and get the GFT roundel for the back window of your truck.
We have use of a cabin in Cotton, MN (recently -35, horray!) which is just down the road from Eveleth and the USA Hockey Hall of Fame. Such a random place for a professional Hall, but whatever. It's not hard to get to at all.
In the Cities themselves, there a fair number of cool things to do.
Go to Minnehaha Falls and SeaSalt to drink beer, eat seafood (flown in everyday from the East Coast, I know the owner) and people watch.
If you are beer guy, go to Surly Brewing for dinner and brews
Museums? Minneapolis Institute of Arts, and the Walker. The only Russian Art Museum in the USA is in south Minneapolis and well worth a visit.
I live out on Lake Minnetonka and a great way to spend a Saturday is on the lake, either in a boat or at any of the bars and restaurants. I'm close to Lord Fletchers but note it can be full of rich aceholes, cougars, slutty college girls and swole bros. Not really my scene so much any more but still worth the time.
Bike the Midtown Greenway or the Grand Rounds Scenic Byway. Or walk around the Chain of Lakes.
Cross the river and explore St. Paul: walk along Summit Ave (beautiful old mansions) & Grand Ave, go to Como Park
If you like things a bit gritty, hit Lake Street in Minneapolis. From west to east you will go from hipster Uptown with gastropubs to urban LynnLake with the only real Mexican north of Chicago, to Cedar Ave with the Somali restaurants. You will be fine unless you're drunk and beligerent on a Saturday night. Most recently some guy dressed head to toe in yellow including hat and shoes tried to sell me DVDs out of his trunk. Something of everyone I guess.
If you come during baseball season, see a Twins game
If you are coming, wait until spring, say May or June. Summer is fine but a little buggy. Fall is spectacular but too short.
Have fun! Welcome to the Land of Sky Blue Waters.