Hello fellow Hoosier! I'm not sure if you're wanting a couple of pit stops to get out and stretch your legs kind of thing or rather a few day stop over, so depending on that answer my list might change, but....
What about Nashville? You could stop a the Parthenon, it would give the kids a good place to get out and run around, plus if you're lucky you might be able to catch a really cool art fair that they have there.
Or Chattanooga, here you could go to Rock City, or to Look out Mtn. I don't know how old the kids are, but I remember loving going there for school field trips as a kid. (used to live in Chattanoogo)
Or Atlanta, if you want a more mid point place. There you could go downtown and see Olympic Park. Or if you like water parks you could go to White Water park.
HTH!