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Lancaster to Columbus: There are two great old highways that you can follow. Start out on US-30, the old Lincoln Highway, west through York PA (which was once briefly the capital of the US) to Gettysburg and its moving battlefield and national cemetery, then use US-15 south to Thurmont MD and get on MD-77 west through Catoctin Mountain National Park (You'll be passing very close to Camp David) and MD-66 to Hagerstown and US-40. Just west of Hagerstown you can visit Fort Frederick and the Chesapeake and Ohio Canal National Historical Park outside Big Pool. US-40 is the old National Pike and is still a great scenic road following the Potomac River through the Appalachian Mountains and as it cuts up through Pennsylvania, it passes the site of Col. Washington's Fort Necessity from the French and Indian Wars. US-40 will run parallel to I-70 from Washington PA to Columbus and so makes a good choice, allowing you to see small towns as time permits, or hopping on the Interstate if you decide to cover some ground more rapidly.
Columbus to St. Louis via Bloomington: I'd probably just stay with the I-70/US-40 combo until well past Dayton as there is no good way through the Dayton/Cincinnati corridor and you and your son might really enjoy a stop at the US Air Force Museum in Dayton. Then at Spiceland IN head south on IN-3 to Greensburg and IN-46 west. Then you can take some smaller roads (IN-45/IN-54/IN-57/IN-58/IN-67) to Vincennes and US-50 to St. Louis.
St. Louis to Wichita: This is easily the most straightforward of the legs, simply continue on US-50 west out of St. Louis to Jefferson City and pick up US-54 from there the rest of the way to Wichita.
As you can see, it's possible to take 'back' roads whichever intermediate points you pick and to find great small towns, historic sites, scenic byways, and interesting stops.
AZBuck