The action of this story is set in the narrator’s home, a suburban house in the USA. Conversations take place between the narrator and his wife in their living room and in the kitchen; and between the narrator, his wife, and Robert (the blind man) on the porch and in the living room. From the clues in the story, we know that the location of this house is five hours by train from Connecticut:
So he was visiting the dead wife’s relatives in Connecticut. He called my wife from his in-law’s. Arrangements were made. He would come by train, a five-hour trip, and my wife would meet him at the station.
We also know that the train trip includes a “scenic ride along the Hudson.” So we can conclude from these clues that the story is likely set in upstate New York.
In addition to the physical setting, we can also consider the time that the story is set in. There are a few clues in the story about the time that the story is set. The first is that the characters discuss the difference between color TV and black & white TV sets and that the narrator and his wife only “traded up” to a color set recently. The second clue is that the narrator’s wife and the blind man communicated by recording themselves on tapes and posting them to each other. This happens for nine years before Robert meets the blind man—the first tape is sent “after a year or so,” referring to the summer that the narrator's wife spent working for Robert. It’s unclear in the story whether the characters are using cassette tapes or micro-cassettes: the narrator only refers to them as tapes. It’s likely that the narrator’s wife and Robert preferred to communicate this way due to the high price of long-distance phone calls at the time.
These two technological clues hint that the ten years described in the story are roughly between the mid-1960s—when the color TV, cassettes, and micro-cassettes became available in the USA—and 1981, when the story was written.