Technically, the setting of the story is the author's farm.  White turned his personal farm into a fictional setting for his story.  We are not told a specific town or area in the story, but we are provided with a description of the farm.  Most of the story takes place on this fictional farm, but there are brief glimpses into other areas of the town.  For instance, Wilbur is taken to a county fair.  We also catch glimpses of the town and the townspeople.  The farm yard setting allows us to see the animals in a particular light.  Wilbur is destined to be food on the table before Charlotte saves him.  We see inner workings of farm life depicted realistically.