1950s; New York City; Boston and its surrounding suburbs
The main action of the story takes place in the summer of 1953. After an internship at a magazine in New York City, Esther ends up in her hometown outside Boston, where she attempts to commit suicide. She then spends much of her time in a psychiatric institution, also outside Boston, before her release in January, 1954.
Esther lives in an America that's emerged flush from victory in World War II as one of the pre-eminent world superpowers. In this post-war period, the American economy is booming, and the middle class enjoys unprecedented prosperity and access to a wide array of consumer goods. We're in the world of Mad Men, where American consumer culture finds its expression in the kind of glossy women's magazines that Esther interns at. (Esther's experience is partly based on Plath's own as a college intern at Mademoiselle.) This period of prosperity also ushers in the baby boom, and to this day, when we refer to "baby-boomers" we're referring to people who were born around this time. (You can read more about this time period on Shmoop History.)
The flip side of this heady period is a deep paranoia toward outsiders as a consequence of the Cold War. After World War II ended in 1945, the United States and the Soviet Union became rivals for nuclear supremacy, and suspected communists were rounded up in the United States on the suspicion that they were spying for the Soviets. The Rosenbergs mentioned in the first paragraph of the novel were casualties of this period, also called the McCarthy era. While recent scholarship has emerged showing that the Rosenbergs were involved in espionage with the Soviet Union, at the time their electrocution was viewed by many as another example of the excesses of the McCarthy era (source). In a time when the memory of German atrocities during World War II was still fresh in the American psyche, Esther's German ancestry contributes to her feeling of isolation from mainstream American society and her identification with the Rosenbergs' fate.