Consider the following sentence:
Sorry for not being at home when they came. I had to be in the city.
The person who says it lives in some city and on that day he/she is still in the same city but has to run errands, not stay at home.
Is “in the city” used correctly in this particular context? Does it convey the idea?
In my part of the world (Australia), this is fine to say.
“In the city” usually refers to being in the central business district where the shops and businesses are. If someone says “I’m going in to the city” it usually implies they are going to this central area to do some shopping or work, even if they technically live within the boundaries of that city.
It is similar to the term “going down town”.