I just realized we never really used the phrase 'the city' where i lived in the Midwest
Back home was way out in the country and people usually said 'I'm going to town' if you were going anywhere but a neighbor's -- which, 'to town' meant going to the nearest place that sold milk. Usually a gas station. There may or may not be a stoplight involved too.
If you were in fact going to a city (which usually meant a place that had public transportation - anything else was 'a town') you'd say the name so people would know which one. Since they were all so far away they practically felt like another state anyway.
Now I actually live in a city (Indianapolis) but it's so spread out I still don't use the phrase, I just say 'downtown' and that means the places where the biggest buildings are. Anything else is 'northside', 'southside', etc. Or y'know, the actual names of the places like Speedway or Castleton.
Huh! I wonder if that's a Midwestern thing, because I just tried to say it and it does feel weird xD
That's not terribly different from life in Richmond, VA. Granted, the South is rather provincial like that. In Richmond, there's the downtown (subdivided into Shockhoe Slip and the Bottom), South Side, West End, East End, Carytown, the Fan, etc. Or even New Orleans: French Quarter, Ninth Ward, the West Bank (or wank; even though it's technically
south of the city) Garden District, MidCity, Metairie, Kenner, etc. I feel like any city has that... in Europe it's generally either the Old Town or the various neighborhoods. Just one more way that people make themselves feel like it's home, and outsiders feel left out.