Missouri is almost as big as Michigan. Where would you recommend I go in Michigan for two weeks and what is worth seeing or doing? Never mind, I lived there for almost a third of my life, I know the Michigan places I like to visit.
What do you like to do? For water sports, there is Lake of the Ozarks, a huge resort area SW of St Louis, but also drawing a KC crowd.
Do you want to visit major metro areas with urban culture, historical significance, city amenities? Missouri has two, St Louis and Kansas City. St Louis is still an old urban center much like Detroit was in the 1950s and early 60s, before Detroit crumbled into a POS. KC is a modern sprawling metroplex in the Houston-Los Angeles-Las Vegas style though not yet quite that large.
Looking for something like Nashville, Dollywood, or a minor scale Disneyworld, or a Las Vegas without the sin? Missouri has the Branson area. The Branson area (Table Rock Lake) also has some very nice water/forest areas on reservoirs feeding the Arkansas river system, though if that's what I was looking for I would go into NW Arkansas or NE Oklahoma, to get the reservoir "wilderness" experience without having to take in the tourist traffic Branson draws.
My own favorite place in Missouri is the Hannibal area, where the Mark Twain connection has made for the historical preservation of a late 19th century river port (most others have either died or evolved into something quite different). I stay there one to three days at a time, often, but have not extended my visits to two weeks or more. If I am not in a large city, I like to keep moving. There is Mark Twain Lake just west of Hannibal, but if I am staying on a lake, it would rather be Lake of the Ozarks in Missouri, or more likely Grand Lake O the Cherokees in Oklahoma.
There is Chillicothe, home of Sliced Bread. St Joseph, starting point for the short-lived Pony Express. Independence (now kind of a KC suburb) home of Harry Truman. If you look around you'll also find the home towns of Walt Disney and General Pershing (all near US-36). Drift over into Atchison, Kansas, and you'll find the birthplace of Amelia Earhart, just across the river from Missouri.
If you follow the route of US-66 (now I-44) you can still find many of the 1950s-60s Route 66 tourist traps and modern additions: amusement parks like Six Flags, large cave complexes, safari parks, the walnut bowls factory, original home of Bass Pro Shops, Precious Moments at Carthage, and a few of the largest motor coach resale and RV wrecking yards in the Midwest. I've traveled this route at least fifty times in the past 30 years, have found many places to visit for a few hours, but none where I would be compelled to stay for two weeks.
So I find Missouri an interesting state, passing through it hundreds of times going to and from Michigan, many places I will stop for a day or two, but no place that might tear me away from home for two weeks. But that's because the places I might stay two weeks in Missouri, the parks on the reservoirs, I have the same thing closer to home in NE Oklahoma.