You asked about routes and places to see. OK, I have in the past gone online and ordered the travel guides from all the states I would be going through on our previous long trips. You have lots of time to do that and have it at hand to look through and see what stands out to you to see and do. They are free. Just look up the dept. of tourism for each state. I like them because they divide the states into regions with region specific maps usually.
From Ohio you could head to Indianapolis and see the Speedway museum. Then head on to St. Louis and see the Gateway Arch and museum. Then make your way to Springfield MO. and see the home of Bass Pro shops and then continue down to Oklahoma City and pick up I-40.
An alternative is to head to Nashville and pick up I-40 there. Mammoth cave is in Kentucky a little way off I-65, then on to Nashville and see the Hermitage there and Broadway street downtown. Onward to Memphis and into Arkansas and Oklahoma. No suggestions for those 2.
Into Texas there is Palo Duro Canyon, the grand canyon of the east. It's not too far south of Amarillo and might make a good place to camp for a day or 2. On into New Mexico and Arizona. We stayed in Williams when we went to the Grand Canyon. Yes, it's an hour drive away but really, if you don't hike or intend to take one of the mule excursions or rafting trips then there isn't all that much to do there. We loved seeing it and we went there 2 days. Williams is a great route 66 town. We stayed at the Grand Canyon Railway RV park. Very nice park with access to the hotel and the buffet restaurant. I will say you may not want to boondock in the hot summer. You need electrical hookup to run the air conditioner
You have almost 3 weeks to do this in. It will be a lot of driving and having to pass up seeing some sights. Get the visitor guides to the states and then you can compare things you may want to see or do. It will be a wonderful trip.