Road trip loop from Chicago to the Carolinas
 

My family will be leaving soon on a two week road trip to the east coast. We have two 13 year olds that will be traveling with us. We would like to travel at a leasurely pace and stop at cities of interest. Having never traveled there before, we are looking for suggestions on what cities would be good to go to. We definitely want to stop in Springfield, IL to see the Lincoln Museum, Mammoth Cave in Kentucky, possibly Nashville, TN, the Great Smoky Mountains, and Wilmington, NC. Suggestions on where to stop and what to see and where to eat would be greatly appreciated. We enjoy beautiful scenery, swimming, music, fun and interesting places to visit.

I'm planning a similar trip in September. My tentative route is CHI to Springfield then across to Indianapolis with a stop for a tour of the Indianapolis Motor Speedway and overnight in Richmond, IN. Next Dayton, OH and the Wright-Patterson Air Force Museum. South on US 68 to UD 52 along the Ohio River. Stopping when it feels rights, maybe Portsmouth, OH, Ashland, KY or Huntington, WV.
The West Virginia Turnpike to Beckey. Maybe overnight and then drive the historic coal route of WV 16 and US 52 into Bluefleid and onto Ashville, NC.
From there spend some time in the Smokies before Knoxville, TN and on to Atlanta. Across to Oxford, MS, then Memphis, TN and Kentucky. I'm skipping Mammoth Cave becasue been there alreayd and visiting some of the whiskey makers in Bourbon county before heading back to Chicago.

You might consider staying in Pipe Stem State Pk in W. VA. and going rafting on the New River. You can stay at a lodge there that is accessible by a furnicular, which the kids would love.

Please plan to spend time in Charleston SC and surrounding area. It is beautiful and unique. It is full of history and a very different climate zone than the midwest- much more tropical. As well as Ft Sumpter and places in town, you can visit plantations and the off-shore islands. Eat boiled peanuts. Lots to do around there.

NC, you might enjoy Ashville, a pretty town in the mountains.

I don't think they are going to Charleston SC--it's pretty far on down there.
For the OP, if you go on to Nashville, and on across Tennessee toward Wilmington, you might want to stop in Asheville, and then Winston-Salem, and see Old Salem. Winston and Durham both have AAA baseball teams that could be fun for an evening.
Heading back home, you might want to come east to charlotte and head home north on i77 (perhaps the Pipe Stem suggestion could be along there) and on to Chicago through columbus, Indianapolis, etc.
To the poster who is doing the Dayton stop--good call on WWright Pat.
The drive along the Ohio River is very pleasant but there is not much along there. You are ambitious to then head for Mississippi.

If you are doing a loop, when you head back home, you could make your last stop Sandusky, Ohio and go to Cedar Point. It is heaven for most 13 year olds.

Another good stop would be Beckley WV for White Water rafting, even though this year the water may be really low. We always went with Class VI River Runners. Our kids loved it and we also had a great time.

I would bag Wilmington unless you have promised the kids time at the beach. It is a great place to retire, but there are better places to go on vacation: to the south, honky tonk Myrtle Beach or upscale Charleston (good beaches on surrounding islands) or to the north, the Outer Banks or Williamsburg.

It's worth trying to get off the interstate in some segments of your trip. I still remember small towns I saw when I was your kids' age. A different world from the one I knew.

Have a great trip. It is a real American journey, wherever you go!

While Wilmington is wonderful, I think Charleston is worth the extra 4.5 hours. Or, you could drive to Wilmington and do both!
I'd do a visit to downtown Charleston and then go visit the Isle of Palms or Sullivan's Island. Take the kids to Partiot's Point and on a carriage tour. On your way home, spend a night at the Grove Park Inn in Asheville and tour Biltmore House.
If you are in the Triangle, I second Gretchen's idea of a night at the Durham Bulls. It is a fun time, for sure! And eat some BBQ while you are here, just to try some Western NC vs Eastern NC style. It's fun to compare the regional variations, and if you go to SC, they have Mustard low country BBQ too!