Well...
If you come through Missouri I would recommend touring the Anheuser-Busch brewing factory. Then have a big plate of toasted ravioli, fried mushrooms, hot wings, and chase it all down with an ice cold Budweiser bottle that hasn't been off the line for longer than a day.
Missouri wine country is also extremely beautiful to tour and explore..
Also, St. Louis Zoo is completely free and one of the top rated in the world.
Do I sound like an alcoholic now?? Lol
Honestly though, I have been all over the country and a good chunk of the world. And if I were on a limited time schedule I don't think Missouri is really a state that I would spend much time in.
Some DEFINITE places to visit: Washington D.C., Florida, the smoky mountains and rocky mountains, Maine, Colorado, Maryland, Texas, Montana, Oregon and North Carolina.
California is pretty much worthless... but it gets a lot of hype.