Short route takes you through Memphis across the river to US 65 to 160 into Springfield MO Then take 13 to Clinton Mo then 7 to I49 into Kansas City MO. Where to camp depends on where the tournament is located.
As to what to do. Along your route is river rafting, Branson/Silver Dollar City, Caves and many lakes.
You have not indicated he age of your companions. That makes a huge difference in what to do in KC. There is the Negro Baseball Museum, Jazz Museum, World War 1 Memorial, Worlds of fun, and many more things to do. I suggest you go to the visitors bureau for Kansas City MO to find many more. Of course there is Baseball in an outstanding ball park.
As to what to eat. Its really what do you like. The area is famous for stakes and BBQ.
Have a nice trip.
Roy