The story is set in a city that has catacombs underneath it, which are narrow passageways that contain old tombs, and where people store their wine to keep it cold and safe. It is most likely in Europe, probably in Italy. These catacombs are dark, dank, damp, and very maze-like, and super easy to get lost in if you don't know where you are going. They are also rarely visited; the occasional person goes down to get some wine, if they have some under their apartment or house, but otherwise, pretty abandoned. They are made of stone, and often in a state of crumbling decay.
It is into these maze-like tunnels that Montresor leads Fortunado. Fortunado is not alarmed by this, because the pretense that Montresor uses is that he has a wine that he wants Fortunado to taste; wine is kept in the tunnels, so he follows him there willingly. They go through Montresor's house, and descend some stairs, and
"We came at length to the foot of the descent, and stood together upon the damp ground of the catacombs of the Montresors."
Montresor obviously came from a long-standing family that had owned that house and those catacombs for a while, because Montresor says they belong to his family, and mentions later that they were "a great and numerous family" when Fortunado mentions that his tombs are "extensive." Montresor leads him further and further until he reaches his goal:
"At the most remote end of the crypt there appeared another less spacious... From the fourth side the bones had been thrown down...we perceived a still interior crypt or recess, in depth about four feet, in width three, in height six or seven."
He chains Fortunado in the chamber, and walls it up, leaving him to his fate. I hope that these thoughts help to to picture the environment that the unfortunate Fortunado finds himself in; good luck!
Montresor has a long-standing problem with Fortunato. We do not know what it is, because we are never told. Montresor knows that Fortunato is a wine connoisseur, and tempts him with an Amontillado - a type of sherry wine. Montresor wants Fortunato to taste the wine to see if it's the real thing. Montresor lures Fortunato into Montresor's family's catacombs in search of the wine. The catacombs are deep underground. Once there, Montresor shackles Fortunato to the wall and proceeds to brick Fortunato into that recessed area.