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.

In order to answer this question, I encourage you to consider how much of the story revolves around the neighborhood.  Speculating how the story would change by changing the location of the Finch house is easier to do by thinking of the things that would not have happened, rather than would could have happened in another part of Maycomb.

One approach to answering this question is to go back to the text and create a list of all of the important events in the story which would not have taken place if the characters lived in another neighborhood.  Here are a few to help you get started:

• Children's curiosity sparked by the Radley house: Mr. Nathan Radley was seen walking back and forth to work in town.
• The day of the trial in court: the children observe what looks similar to a parade of people walking right down their street to the courthouse.
• Relationships with other characters in the neighborhood are close because "in town" the houses are physically closer together than they would be "in the country."  Consider the vast experiences and lessons Jem and Scout receive simply as a result of neighborhood connections; Miss Maudie's fire, meeting Dill in Miss Rachel's yard, interactions with Mrs. Dubose, the Radley house (again).
• The night of the mob scene: The children's ability to follow Atticus to the jail that night.
• Distance and direction to and from school: the climax of the novel (the attack by Bob Ewell) would have been far different (possibly worse) if the Finches lived somewhere else.
• Finally, the idea that where a family lived was also associated with the family's position in society.  Consider that another neighborhood would likely mean another profession for Atticus and a completely different social structure for the main characters.