Columbia (nickname CoMo) is a college town right in the middle of Missouri. It has about 110,000 residents, about a third of which are students, mostly at the University of Missouri. The university campus is beautiful, and it's located right next to the downtown area. It's an interesting place, because it has a very large fraternity-culture presence (campus and downtown) intermingling with a large hippy-culture presence (downtown).
If you go there, hit up Ragtag Cinema downtown. It's an indie movie house attached to a bakery, bar, video rental, and record store. Home to the art scene in Columbia. Shakespeare's Pizza downtown is also great. Best pizza in town and good, cheap beer. Ground zero for both bro and hipster scenes.
North or South toward who-knows-where
You can start from where E Broadway meets Highway 63. There's an onramp with not too much space for drivers to pull off. Traffic is enough to be regular but slow enough that a car won't be afraid to stop and pick you up. I've had decent success from this spot.
East toward St. Louis
I've never hitched east or west out of town, but if you're going east, I would definitely suggest starting where Business Loop 70 trickles into I-70.
West toward Kansas City
Going west, a good bet might be where Stadium Blvd meets I-70. Lot of traffic there.