<p>To quote the New Oxford American Dictionary: </p>
<p>"neighborhood |ˈnābərˌhoŏd| ( Brit. neighbourhood)
noun
a district, esp. one forming a community within a town or city : she lived in a wealthy neighborhood of Boston.
• the people of such a district : the party disturbed the whole neighborhood.
• neighborly feeling or conduct : the importance of neighborhood to old people.
• the area surrounding a particular place, person, or object : he was reluctant to leave the neighborhood of Butte.
• Mathematics: the set of points whose distance from a given point is less than (or less than or equal to) some value. "</p>
<p>I would go for it, but you can decide for yourself 
I doubt they are going to be nitpicking, the question is trying to find out how the place you grew up in and people you grew up with shaped who you are and it sounds like your response will answer that</p>