When I'm in Cincinnati I have to have Skyline. When I'm in Dallas I have to have Whataburger. When I'm in Minneapolis I have to have Caribou Coffee, or any airport I'm in where it's an option. The two I have that aren't really regional but I try to stop whenever I can is Waffle House and Steak N Shake.
Not really fast food but whenever I'm in Chicago I try very hard to get to a Gino's.
Portillo's has a location in Minneapolis as well, I like them, but if I'm actually in Chicago I'd much rather go to a local stand than Portillo's.