Daisy Miller by Henry James does not really portray America, per se. The entire novella is set in Europe. The main "American" characters represent a small subset of Americans of British descent living in Europe. No Native Americans, African Americans, or even Americans of varied European heritage are portrayed.
The eponymous heroine Daisy Miller is a wealthy young woman who can be viewed as either refreshingly innocent or hopelessly spoiled and self-indulgent. Her manners are free of many of the constraints of the more formal upper class European society into which she is introduced. Most importantly, American upper class society places fewer restraints on the behavior of young women than European society. Unchaperoned interactions between young women and men are more permissible in Daisy's American social circles. He manners are freer, more spontaneous, and less formal than those of her European peers.
The main genuinely European character is Giovanelli, portrayed as a sophisticated con man who takes advantage of Daisy's innocence. Representing European cultural values, ironically, are Frederick Winterbourne and Mrs. Walker, who are actually expatriate Americans who have assimilated to European manners and values. Mrs. Costello also is appalled by Daisy's improper manners.
In terms of America itself, it is portrayed as a place of greater social freedom and mobility than Europe, with greater economic dynamism, but also as being cruder and more materialistic. Europe is portrayed as more sophisticated, but also ultimately corrupt, narrowly conventional, and less dynamic.