To answer your question, let's define milieu as both a social setting and the place, or in the case of The Sun Also Rises, places where the story develops.
The main characters in the novel are expatriates from the United States and Britain who are living on Paris's Left Bank, a mecca for artists, writers, and intellectuals, in the decade after WWI. It was a time and place devoted to "cafe society" as creative, free-wheeling people from all over the world congregated to exchange ideas about art. Ernest Hemingway was a part of this scene and the novel is considered a roman a clef. Feelings of disillusionment caused by WWI plague this group, and they struggle to find purpose and meaning in their lives. Drinking plays a major role in their efforts to cope.
The Americans include Jake Barnes, the narrator, a wounded WWI veteran working as a journalist. Robert Cohn is a wealthy American Jew who has come to Paris to write. Bill Gorton, another WWI vet, comes for a visit but is not an expat.
Lady Brett Ashley, a British socialite, is at the center of many of the conflicts that play out in the novel. She is a drinker, and promiscuous, yet desirable. Jake is in love with her, but she is unwilling to commit to him because of his impotence from his war injury. She takes up with Mike Campbell, a Scot who is struggling with financial problems, alcohol, and anger. She is also briefly involved with Cohn.
Count Mippipopolous is a wealthy Greek who becomes another one of Lady Brett's lovers; unlike others involved with her, he is not jealous and doesn't try to make their relationship exclusive. He is perhaps the epitome of a Left Bank Parisian at this time; he is a pleasure-seeker who is interested in the world of ideas and rejects conventional attitudes about morality.
Pedro Romero is a handsome nineteen-year-old bullfighter that this group encounter when they travel to Pamplona for the debauchery of the fiesta and bullfights. Lady Brett briefly takes up with him and then leaves him behind.
Spain is meant to represent a country still clinging to its religion and traditions. Hemingway means for it to contrast France, which has been altered significantly by the war, and whose capital, Paris, is filled with "the lost generation."