If your work requires internet access, take care to ensure you have plans in place for that wherever you stop for the week. In many campgrounds your best bet (though not always inexpensive or exceptionally quick) would be via the cell network; but not all state parks have great or any cell phone reception. That's just generally speaking, of course.
In terms of places to stop, St Louis comes to my mind. Several nice traditional museums, a good zoo, the arch, and the not-to-be-missed City Museum that I personally think is cooler and more fun than Disney...not that they're quite aiming at being the same thing.
As an 8 or 9 year old, I really enjoyed cavorting around the Badlands. Mt Rushmore, on the other hand, struck me (and still rather strikes me) as somewhat "meh," something I'm content to only see in passing.