Since there is no overt statement that indicates the setting, the reader must surmise from the characters and dialogue what is the time and place of Wilde's "The Young King." Some of the indications that this story is set in medieval times are the references to cathedrals, the bishop to conduct the coronation of the king, the peasants who toil on the loom and the usage of Middle English: "the Chamberlain spake..."
While there are several references to items having come from Venice and an Italian poison, the mention of a "stout Burgomaster [who]had come to deliver a florid oratorical address on behalf of the citizens of the town" indicates the place of the story is not Italy. "Burgomaster" (Burgomeister-alternate spelling) is of Germanic origin meaning the chief magistrate of a town, so the country where the young boy is to be made king, is likely a Germanic one.
Since Wilde's tale is a fable, the setting is probably an imagined one, a composite of those used in fairy tales and such.