The setting of Slaughterhouse-Five is wide-ranging, but the two most important places are Germany during World War II and "Ilium," the fictional town in upstate New York where Billy Pilgrim lives most of his life.
In Germany Billy undergoes the painful experiences of captivity and violence that cause him to start skipping through time. And it's the narrator/author's real-life time in Dresden, Germany, that provokes him to write Slaughterhouse-Five in the first place. In Chapter 1, the narrator tells us that he and his wife spent some time after the war in Schenectady, New York, which Billy Pilgrim's "Ilium" seems to be based on. The parallels between the narrator and Billy's wartime and postwar experiences add to the sense that Slaughterhouse-Five, for all of its aliens and time travel, is a largely autobiographical novel.
Another recurring setting throughout the novel is the hospital. Billy spends his first night in the POW camp in the hospital, where he meets Edgar Derby doped up on morphine. When Billy has his breakdown and checks himself into a veteran's hospital after the war, he meets fellow veteran Eliot Rosewater and discovers the science-fiction novels that will help him escape from his awful life for the next 30 years. And when Billy is recovering from his plane crash in a hospital in Vermont in 1968, he first begins saying the name "Tralfamadore" aloud.
These three scenes of recovery strongly associate hospitals with relief. At the same time, these moments of rest from the stresses and memories that are driving him crazy are only temporary. Once Billy leaves the hospital, he always loses control again: his release from the prison hospital allows him to be shipped to Dresden; his departure from the veteran's hospital leads to his marriage with Valencia and the start of his dreary life as an optometrist; and his escape from the Vermont hospital sends him directly into conflict with his daughter, Barbara. While Vonnegut seems to represent the work that doctors do positively, medicine is still not enough to heal Billy of all that ails him. For that, the entire world would need to change.