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Mapquest says it is about 1019 miles between the two cities (about 16 hours driving time), so the half-way point would be near the middle of Missouri.
If you are looking for a place to stop during a drive at the half-way point, you could stop anywhere between St Louis, MO and Springfield, MO. Some towns about half-way between there are: Rolla, St Robert (Fort Leonard Wood), and Lebanon, MO.
The major airport about half-way is at St Louis. Other airport half-way options would be Kansas City, Fort Leonard Wood, and Springfield, MO.
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