What can you do in Missouri?

I would visit the Missouri tourism site and find which city you're going to.
Just google "Missouri Tourism Official Website".

Some popular attractions in Missouri include:

Jefferson National Expansion Museum (aka the Arch) in St. Louis
Branson, MO has many attractions, including a theme park (Silver Dollar City)
There are many caves in Missouri.
Hannibal, MO is the hometown of Mark Twain. It has some attractions and museums.
In Lexington, MO, there is a Museum about a battle that took place there during the Civil War.
Old Route 66 also passes through Missouri.