Okay, after looking at your itinerary (and not mentioning the things you've already mentioned/have been suggested), I would suggest:
Chicago: Super Dawgs, the best hot dogs you'll ever eat! If you're not in the mood for hot dogs, an Italian Beef Sandwich is a must. You can't leave without trying one or both of them!
Salt Lake City: The Beehive House, where polygamy reigned supreme!
LA: Do the whole tourist thing! Mann's Chinese Theatre, etc. Marilyn Monroe's star is in front of the McDonald's.
Texas: Try chili made with armadillo. It's kinda skunky, but you'll be able to say you tried it!
MidWest: Whataburger is another great chain not mentioned. So is International House of Pancakes (IHOP).
Columbus: Home of the first American Soccer-Specific Crew Stadium. A fellow Canadian works in the front office and may get you a discount!
I won't add more - you've gotten plenty of ideas! Oh, there's a book that has goofy sites, like where the largest ball of string is - I'm sure someone knows the name. Have a safe & wonderful time!!