Sounds like you've already got one
Considering your money/timeframe, and what you want to do, I think you've already got a pretty good itinerary mapped out.
In terms of a "final destination," it already sounds like you've got a good plan towards making it the Black Hills. Considering you'll spend a full day driving there and back, that would give you five days to explore the area. Which if you hit Badlands, Custer, Rushmore, Crazy Horse, and Deadwood would be a nice leasurely pace. You could also check out Devils Tower in Wyoming and/or Teddy Roosevelt NP in North Dakota before heading back.
Now that said, if you really want to see Yellowstone, you could do it in a week, but you'd probably have to skip some of the things you mention like the Badlands or Custer. Its a pretty solid two day drive from Minneapolis to Yellowstone, so giving yourself a week, you'd basically have 3 days to enjoy yourselves. Since places like the Corn Palace, Wall Drug, and Deadwood are all on the way, you could probably stop at them briefly, but you'd have to plan it a little more carefully so you don't get to those places in the middle of the night.