Daisy Miller opens at a grand hotel in Vevey, Switzerland. The narrator explains that this town in Switzerland, and this particular hotel, Les Trois Couronnes, is a popular tourist destination; it resembles places like Newport, Rhode Island and Saratoga, New York, in the way that wealthy Americans migrate and spend weeks at a time there in the summer—it seems as if the upper crust of New York society has wholly relocated to Europe.

A young American man named Frederick Winterbourne, who came to Vevey to visit his aunt at the hotel, is sitting in the garden and admiring the beauty around him. A small, rambunctious boy approaches him and asks him for a lump of sugar. The boy, Randolph, introduces Winterbourne to his older sister, Daisy. Winterbourne is immediately attracted to her beauty and introduces himself, but he is also concerned with whether it is proper for him to speak to a young lady who is unattended by an adult.

Daisy immediately piques his interest, not only because of her beauty, but also because of her behavior. She presents herself with a strange mix of innocence and boldness. She looks directly at him, not at all shy, but not immodest, either.