Being from Jeff City and knowing both MCI and STL airports, it is really no big deal which city you fly into (STL is closer by about an hour just because MCI is so far north). I-70, the main interstate, is going through some major roadwork around STL (I was there just last week) that is not going to end anytime soon. I have found that it is cheaper to fly in/out of MCI than STL if price is a factor.
As to what to do in Jeff city...nothing much. It is a city with about 40K, mostly state workers. You can tour the capitol building (It really does have an interesting history--the 1st two capitols burnt down), or play golf. Eagle Knoll is about 15 mintues away and is one of the best courses in the state.
As mentioned in the post above, Madison's Cafe is a nice Italian place to eat. I would also have to recommend Pizzaria Napolitana (Greek). I eat there often and am never disappointed.
Lake of the Ozarks is only a 45 minute drive from JC. They have a HUGE outlet center (I think close to 150 stores--Polo, Reebok, Levi, and other well-known stores). It is a great place to go shopping.
Hope this helps!