Alice Pike Barney and Natalie Clifford Barney
In 1882 Alice Pike Barney and her family spent the summer at New York's Long Beach Hotel, where Wilde happened to be speaking on his American lecture tour. Alice and her daughter Natalie had a chance meeting with Wilde and they spent the next day with him on the beach. The meeting turned out to precipitous for the mother and prescient for the daughter.
For Alice, her conversations with Wilde changed the course of her life. He inspired her to pursue art seriously despite her husband's disapproval, and she would go on to study under Carolus-Duran and James McNeill Whistler, and later wrote and performed in several plays and an opera, working to promote the arts in Washington, D.C. Many of her paintings are now in the Smithsonian American Art Museum. For Wilde, whose stated aim on his tour was to introduce the arts to America, this achievement, unknown to him, must be regarded as a great success for his mission.
Natalie Barney, the daughter, was five years old at the time of the meeting with Wilde. In her memoir Aventures de l'esprit (1929) she records what she nominates as her First Adventure: the story of how Wilde scooped her up as she ran past him fleeing a group of small boys, and held her out of their reach before sitting her down on his knee to tell her a story, what she recalled as "a wonderful tale". 
Thus was established a series of connections with Wilde. Natalie Clifford Barney became a playwright, poet and novelist resident in Paris where she held a salon on the Left Bank for more than 60 years. Her time in Paris, as art student and then as a salonist covered Wilde's time in exile there, and she served on committees "that commemorated both his birth and death" (Schenkar).
Natalie Barney was openly lesbian as early as 1900 and began publishing love poems to women under her own name. At least two of her lovers had Wildean connections.
The first was a brief affair with Olive Custance, future wife of Wilde's lover Lord Alfred Douglas. Through this relationship Natalie came to know Douglas, and she befriended him during his visit to Washington DC, later becoming godparent to Douglas' and Olive's first child Raymond.
Much later, in 1927, Natalie met Dorothy Ierne Wilde, known as Dolly Wilde, who was Oscar's niece. She was the only daughter of Wilde's brother Willie. The relationship was a passionate one for both Natalie and Dolly and continued until the latter's death in 1941.
 Mentioned in Truly Wilde: The Unsettling Story of Dolly Wilde, Oscar's Unusual Niece, by Joan Schenkar. Virago, 2000. p 151. Fully recounted in Wild Heart: A Life: Natalie Clifford Barney and the Decadence of Literary Paris, by Suzanne Rodriguez, HarperCollins, 2003. pp 30-33. Both these biographies source Barney including Aventures which is regarded as primary source