I'm a Mizzou alum, lived there after graduating for 12 years, now one of my daughters just graduated....get back there several times a year...
Booches for burgers and chili; an institution, been there over 100 years, I think. https://www.facebook.com/group.php?gid=43413726672&v=wall#!/group.php?gid=43413726672&v=info
Ernies for breakfast, as well as Broadway Diner http://www.discoverthedistrict.com/members/ernies.html
There's also a good breakfast spot at Broadway and 6th, I just can't remember the name right now....
Shakespeare's is a must for pizza, their best pie, IMO, is the thicksliced pepperoni, and red onion. Good combination. http://www.shakespeares.com/index.cfm
Another pizza option, and a real friendly place is, G & D Pizza at Stadium and Broadway. Good gyros there, too, as well as reasonable steak. Been run by the same Greek family for years. http://www.gdpizzasteak.com/index.html
Flat Branch is a good brew pub. http://www.flatbranch.com/home.asp
Harpos probably the best college bar in town. http://www.harposcomo.com/
For a little nicer dining, Bleu on South 8th Street has been good for us; have had a few family celebrations there. http://www.bleucolumbia.com/
Kaldi's has good coffee, if you are into that coffeehouse thing. http://www.kaldiscoffee.com/
If you want to visit a winery, a short drive away is this one http://www.missouriwine.com/
And for toasted sub sandwiches that put any chain to shame, try the Sub Shop. http://www.subshopinc.com/index.html
The veggie, sausage and kraut with swiss cheese, Rueben, and the pizza sub were always favorites of mine.
now I'm hungry.