I don't know if the usage is the same everywhere or whatnot, but one of my favorite sociolinguistic beats is simply "The City."
What I mean is this: in most places I've lived, people locally talk about "going to the city" (but implicitly The City) without saying what city. That's because this pretty much always means one specific city, and everyone knows which one it is. They might also refer to "going to town" and this might refer to The City, but might also be a completely different place, also unnamed but not quite as absolutely obvious.
For instance: I grew up in Blaine, Washington, which is simultaneously in sight of the Pacific Ocean, the Cascades/Mt. Baker, and Canada (this is the coolest thing about it). It's mostly remarkable for the Peace Arch border crossing between the USA and Canada, which is the busiest on the US/Canada border until Detroit IIRC (though Blaine itself is a small town). When I was growing up, "we're going to spend the day in the City" almost invariably referred to a day trip to Vancouver, BC (metro population: 2.6 million), while "going to town" generally meant going to Bellingham, WA (population: 94,000). Very occasionally it might mean Blaine itself if you lived on the really rural outskirts).
OTOH, I lived more or less near Portland, OR for many years— sometimes in close suburbs like Beaverton or Tigard, sometimes a little further in places like St. Helens. Regardless, "we're going to spend the day in the City" meant Portland, but "going to town" without elaboration often meant Portland, too (though not as invariably).
Anyway, I've always been fascinated by the concept of "The City" as this unnamed but usually entirely unambiguous reference shared by large numbers of communities. People sometimes mock generic fantasy conventions of people just vaguely referring to "the City," "the Great Road," "the River," etc but this is 100% how people actually talk in my experience. I don't know how far it extends, though.