Being so near St. Louis, the things you get here and no where else are Imo's Pizza (a very thin crust with Provel cheese), Toasted Ravioli--It is normal except toasted and then covered with herbs & parmesan and usually served with marinara sauce, and Ted Drewes' Frozen Custard. There are probably other St. Louis specific dishes but I'm not originally from this area & not too impressed with the ones mentioned above so others may have just gone in one ear & out the other.
I do know that driving around through the city of St. Louis, you will see lots of different signs on little hole-in-the-wall places for all kinds of soul food, Chinese, delicatessens, fresh fish, pit barbecue, pulled pork, etc. These are almost always in not so nice parts of the city and there is no way I'm stopping to eat at one without a team of pistol packing football players with me.
The places remind me a little of the "cocinas economias" in Mexico. Little sidewalk stands in front of the homes that serve really cheap lunches to anyone walking through the neighborhood except the neighborhoods were much less scary in Mexico.