"The Nightingale and the Rose" was written by Oscar Wilde, an Irish author of the 19th century. In the story, the young man is identified only as a student. He is a good student, being very well read. He seems to have a very romantic nature, but proves to be an extremely shallow and self-centered person. The work is a fable rather than a realistic story. As such, the setting is non-specific: a garden, a natural landscape, and the student's professor's house.
Written by Oscar Wilde, however to answer your other question there was no setting specified, but since Wilde was an Irish author I would assume it would be possible that it might be in Ireland, Wilde also spent some time in England it is possible it could be set there as well.