I recently did a mini trip with family from Texas to Green Bay in Wisconsin and enjoyed every bit of it. Anyone else planning to do a similar drive, a few places I would suggest seeing along the way are: the Gateway Arch National Park in St. Louis, G W Exotic Animal Park (If you come up I-35, to Oklahoma City), the Cherokee Strip Museum (close to the Oklahoma/Kansas border), the National Teachers' Hall of Fame in Emporia, and Green Bay Packers Hall of Fame in Green Bay.
The main route (I-35N) goes past 4 states: Oklahoma, Kansas, Missouri and Iowa. I've never driving from texas to Geen Bay but I can suggest cool places to see/visit there like the National Railroad Museum on South Broadway and the Neville Public Museum. Even if you are not into railroad history or natural history, you will enjoy the exhibits there.
I would recommend stopping off in Milwaukee if you're coming to Green Bay from the South. I just adore that city...the Public Museum is really fantastic and you can't beat the art museum with the wings that move throughout the day. It's right on Lake Michigan...and the city's fairgrounds are there too. There's always a festival there. I totally love Summerfest. That might be the most fun festival I've ever been to.