Márquez never specifies the time or place of his story, but if you're familiar with his other works you can guess that the action takes place somewhere in Latin America. Given the villager's mythological associations (like Estevanico), this doesn't seem like a bad guess. We know that we're dealing with an isolated village, with no real modern technology, that relies on fishing for its livelihood.
It's important to note the way the scenery changes from start to end. At the story's beginning, the village is simply a "desertlike cape" with "no flowers." Later we're told that it's "arid" and "windless" (9). This is a dry, ordinary, boring place to live. It's so ordinary, in fact, that the drowned man, a truly extraordinary guy, has no place in it. Esteban is incompatible with the village as it first exists. And so with his arrival, Esteban transforms the village into a place as extraordinary as he is. The villagers' plans at the story's conclusion are just that: to be worthy of the drowned man. Make sure you check out "What's Up with the Ending?" for more.