Plenty of Time to Explore
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St. Louis to Minneapolis is only 600 mile or less, depending on how you go and there are lots of possible options for routing and stops, so lets just run down a few of the more intriguing (at least to me) of those possibilities. You could follow the Great River Road all the way up, you certainly have time and there is no shortage of great sites to see including Hannibal, Keokuk, Nauvoo, Effigy Mounds National Monument, and any number of state parks and national wildlife refuges. If you opt for this, the slowest of the routes, halfway would be around Dubuque, but this would really be a drive where you should plan to spend your relaxation time en route rather than once you stop for the day, and with a majority of the sites on the first day, you might want to plan on only getting to the Quad Cities.
A more direct route would follow the Little Dixie Byway portion of the Great River Road up to about Keokuk, but then use US-218 up through Iowa by the Amana Colonies and finish up using I-35 into the Twin Cities. This is the route to use if you find that you have less time than you would have liked. You can overnight anywhere in the Amana - Iowa City - Cedar Rapids area. Each of those towns offers something unique. Amana is at the heart of the aforementioned Amana Colonies, Iowa City is a college town with all that implies, while Cedar Rapids is the second largest city in the state and has a vibrant arts scene.
One other route is worth mentioning, and that is to swing east a bit using I-55/I-39 up through Illinois into Wisconsin picking up I-90 in Madison for the rest of the way to Minneapolis. The Illinois portion of this route would take you through some towns associated with two past Presidents, Lincoln and Reagan, while the Wisconsin portion includes the scenic campus of UW, the river carved rocks that make up Wisconsin Dells, and a rather unique Circus World Museum in Baraboo. Halfway would be Janesville, but I'd probably push on to Madison for a better ambiance with the campus on the lake.
Any one of those would make a great RoadTrip, so while you can pick any of them, you can't make a bad choice.
AZBuck