Our entire story takes place in Pelayo and Elisenda's courtyard. (In fact, it's almost like we're held captive.) But, even though we never go anywhere else, we can gather some clues about the larger setting.
(1) We can be pretty sure it's in a Spanish-speaking country because of the characters' names, and we know it's on the coast, because of the rotten shellfish and the references to the sea. Since Gabriel Gárcia Márquez is Colombian and usually wrote about Colombia, it wouldn't be too much of a stretch to suppose that the town is somewhere on the Colombian coast.
(2) The town where the story takes place is a one-stoplight, two-horse town; the kind of town that you can't wait to get out of. The place is always flooding and filling with rotting shellfish, and people have nothing better to do than look at a mangy old angel all day. It's the kind of place that probably has a roller skating rink that hasn't been updated since 1983, and one movie theater showing movies that have already come out on Blu-Ray. We know this because, well, a captive might-be-angel is apparently the most exciting thing that the villagers have seen in months.
(3) It's hard to say when this story might have taken place. We know that people are still interested in seeing sideshow acts when carnivals come to town—but that doesn't really place it, because that goes on today.
But the narrator does sometimes says "in those times," like when he says that "Elisenda bought some satin pumps with high heels and many dresses of iridescent silk, the kind worn on Sunday by the most desirable women in those times" (11). Using that phrase gives the story an old-timey, once-upon-a-time feeling that we can't quite nail down without more information.
(4) Finally, the characters seem to be living in an environment that's strongly ruled by both the Catholic Church and popular mythology. The wise neighbor woman has her own ideas about who angels are and what should be done with them, while Father Gonzaga represents the official, Catholic side of beliefs about angels.
Nothing, really. It's an almost-but-not-quite real setting that could be anywhere or nowhere. And we think that's on purpose. This is a small, unnamed town, in an unnamed time, with culture that's a blend of local tradition and global Catholicism. It could be any of hundreds—or probably thousands—of small, South and Central American towns. (Not to mention small U.S. towns, if you replace the Spanish with English and the Catholicism with Protestantism.)
Think that an angel could never land in your backyard? Well, says Gárcia Márquez, you might want to think again about that.