The first half of "The Tell-Tale Heart" takes place inside a house with no reference to a city or country setting. However, once the murder occurs certain elements let the reader realize that the murder has taken place in the city setting. A reference is made that four hours pass in the interval of the murder and the arrival of the police. To the modern reader, that may seem a long time for a murder response, but it would have been quite quick in the 1840's. A shriek had been heard by a neighbor- houses in the country at that time would have been so far apart that a neighbor could not have heard a shriek. Also, a complaint had been registered with the police. In the time of no telephones, this would have required someone to investigate sufficiently to realize that they could not determine the origin of the shriek, find it sufficient ground to act, physically go to the police station or at least find a police officer, register the inquiry and then have the police determine there was sufficient reason to ask to enter the home. In a country setting, this would have been impossible because it would have likely required a horse ride through the woods or forest at night; on certain nights, especially one black as pitch the way Poe described it, this would have been impossible.
Also, the police are told by the narrator that the old man is absent in the country. This was a common practice for older people living in the city were to get away to the country for their health.