I would recommend flying into STL and renting a car. Until several months ago, Ozark Airlines flew into COU from DFW, but this airline is gone now. Now only TWE flies into COU from STL, and their service (I believe they are flying J41's now) is not the most reliable. While COU is less than 20 miles from Jeff City (airport is between Columbia and JC), flying into STL and driving from there (2 hours, first I70 West then taking Hwy 54 at the Kingdom City exit) makes more sense and usually saves some $$ on the airfare.
Jeff City is the capital of Missouri. It's not very big on the entertainment side (politely said). Madison Cafe (in downtown JC, close to the Governor's mansion) is a good lunch or casual dinner destination.
If you have a car, Columbia is about 30 minutes away (it's a nice University town), or you can drive to the Lake of the Ozarks (about 40 minutes away) for some water R&R.
Let me know if you need more information.
<Edited for typos>
[This message has been edited by Eugene (edited 08-05-2001).]