The setting of To Kill a Mockingbird is essential to the story. Harper Lee did a wonderful job of choosing a time period and very precise location in which to set her story, all of the way down to the relation of the Finch home to its neighbors. Had the house been located on another street of Maycomb, a great deal of the plot would have been different.
One of the most significant differences that would have resulted from a change in location would be the inability of Arthur "Boo" Radley to watch the Scout and Jem from his home's front window. Had Boo been unable to observe the Finch children and, thus, to develop a relationship with them (at least in his mind), the children would have fallen prey to Bob Ewell's attack. In fact, the children probably would not have been as fascinated with the mystery of Boo Radley, which would have greatly impacted many events within the novel.
Had the Finch household been located elsewhere, Mrs. Dubose, Miss Maudie, Miss Stephanie, and most other important characters would have played very insignificant roles in the story. Their relative proximity to the Finch family enabled them to be considered important and influential, whether good or bad. In addition, events such as the wanderings of the rabid Tim Johnson and the revelation of Atticus Finch's prowess as a sharpshooter would not have warranted as much attention as they received had they taken place in a less prominent location. Of course, there are many other events that would have been influenced or negated by a change in setting.