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You can certainly see a lot of the things you are looking for along the way. I'd say your bet bet for a route that will satisfy your goals would be to take I-70 to St. Louis and then follow the path of Route 66 by taking I-44 and I-40 west.

However, you should know that while you could make this trip in 3 very full days. You would have to have to be on the road for 12+ hours for each of those three days. That is quite a bit more than we generally recommend for an leasurly trip, and it really leaves no room for any sightseeing. If you want to take time to stop at historic sites, like the Oklahoma City Bombing Memorial, pop into a national park, like the Petrified Forest or the Grand Canyon, or just make a random stop to stand on a corner in Winslow AZ, you're really going to need closer to 5 days, minimum to make this trip.