First, a bit of background: Edgar Allen Poe was an American author who was born and raised in Virginia, and later spent time living in New York City and Philadelphia. He died in Baltimore, Maryland. His stories are often not specifically set in one city or another; Poe's attention to setting is focused more on the specific houses/rooms/etc. that his characters inhabit, and the particular atmospheres these domains create. Additionally, in Poe's stories, the first-person narrators (as he often employed such characters) suffer from various mental problems, and seem to confuse fantasy and reality. They re-construct the world, and this reconstruction confuses the audience in regards to what is real and what is imaginary. In some ways, the characters' minds become a "setting."
"The Tell-Tale Heart" is told retrospectively, which means the character is remembering the story rather than living it. He seems to be recalling the events while locked up in a prison or mental institution. He tells of living in a house with an old man (probably a close relative, though the elderly man is never specifically identified). The two seem to live in a normal-enough house. They have neighbors who later call the police; this indicates that the neighbors live close enough to hear and/or see anything unusual that goes on. This proximity, at least in Poe's time, implies an urban setting.
In summary: the story's action takes place in a home--or, at least, the character tells us this. However, there are other aspects that inform the setting. He is delivering the monologue from a jail or psychiatric facility; that is another setting. Finally, his mind is also the "setting" of the story, in that he is creating it there--we cannot be sure what actually occurred, where it occurred, or if it even truly happened at all.