Henry James issues the reader a direct challenge to determine Daisy Miller's system of values, or value system, in Chapter 1 of Daisy Miller, when Winterbourne, upon first seeing Daisy in the distance, says of her, "American girls are the best girls!" a remark instantly rebutted by Daisy's brother Randolf who says, "My sister ain't the best!" The novella then proceeds to examine the idea of whether Daisy is the best or not the best of girls. James makes one thing perfectly clear at the end of the story when at Daisy's graveside Giovanelli says unequivocally to Winterbourne that Daisy was the "most innocent" of girls; this refers to her moral innocence and purity. So the first thing it is possible to ascertain is that Daisy's value system stressed moral integrity and purity that in Daisy's case sprang from moral innocence.
The rest isn't so easy. When going with Winterbourne to Château de Chillon, she accepted the idea of a chaperon however nowhere in the rest of the novel does she actually appear with a chaperon. Mrs. Costello brands her as common and on the steamer to Chillon, Winterbourne has to agree, although her charm overrides her commonness in his eyes. In Italy, she willfully goes unchaperoned when visiting all around Rome escorted by Italian men, a prime offence in English society. In conversation with Winterbourne, she points out that she has a great deal of being in company is social gatherings ("society") in America, yet among the English tourist, she causes herself to be ostracized. Daisy is unembarrassed when in public with Winterbourne or her Italian cavaliers. She has what Winterbourne thought of as a "habitual sense of freedom," and required "a little fuss" of attention" from her admirers.
So it seems Daisy's value system, along with moral purity and innocence, includes guilelessness--what you see is what you get--and its converse being that what Daisy saw is what Daisy expected to get as the genuine article: society was to be as lovely, charming and genteel as it appeared to be. Her value system includes an unstudied freedom and independence: she didn't try to be these things, she just was by virtue of her American background. It includes trust. It includes the expectation of sincerity and genuine affection. It also very much includes the notion of making just enough trouble to get "just a little fuss." James indicates in Daisy's character that her value system is a double edged sword. On the one hand, it is good to not judge superficially or cruelly, as she was judged. On the other hand, having Daisy's inability to comprehend the dangers and risks in friendships and situations can lead to disastrous ends, such as Daisy's death.
Daisy Miller is a young woman who embraces life with full vigor and curiosity. She responds to the world around her through her senses, her feelings. She does not consult convention or tradition to see how she is supposed to behave. She responds with a natural easiness that makes her very different from European girls, and even American girls who follow the rules for Americans in Europe.