The only setting that is detailed in Coraline ("I asked you not to call me Caroline.") is the house and garden, the school is referenced but never visited. Thus, in the narrative, the setting is the bit of the old house that Coraline's parents own, the bits her neighbors own, the garden and old tennis court and the "other" old house and garden where the "other" mother and the dead children with stolen souls live. Yet there are textual clues as to the larger, unspecified setting surrounding the house and garden, bearing in mind that setting includes both where and when, location and time period.
The first clue in the text is the language used by Miss Spink and Miss Forcible. Their syntax and vocabulary marks them as speakers of a British dialect. Their syntax reveals a reversal of person order: In Standard English, the other person is named before the speaker names themself, as in the correct order "both Miss Forcible and myself." Additionally, the expressions they use are typical British idioms and terms: "trod the boards, luvvy." So our first clue suggests the larger setting is in Britain, probably in England. That the main interest in the story is a house and garden with a bored girl tends to confirm a location somewhere in England.
"You see, Caroline, ... both myself and Miss Forcible were famous actresses, in our time. We trod the boards, luvvy."
Our second clue comes from the things Coraline finds in the garden. She finds a "rockery" (though it is all rocks), which is a planned garden of plants tucked in among rocks. This is a very English sort of garden and a very English sort of word describing it. She finds a "hedgehog," which is a very popular animal to find in gardens and in the countryside in England.
The third clue is the general language used by the narrator and characters. Coraline says she wants to "carry on exploring." The narrator says she finds a "haughty black cat." The narrator also says Coraline wants to explore to find the well that she has been warned to stay away from so that she can "keep away from it properly." This language comprises expressions that are common in England.
The fourth clue gives us the time period, the when, of the narrative. Coraline is told by her mother to "play a video." When Coraline turns on the television, all she finds are "men in suits talking about stock markets." The narrator explains that Coraline's parents work by "doing things on computers."
All these clues tell us the that the larger setting, the one not directly mentioned in the story, is England in the contemporary era, the era of work-at-home computer jobs and videos and men in suits talking about stock markets.