I do not find Miss Emily eccentric as much as too rooted in the past. As amy-lepore said above, she has remained stagnant while the town and people are changing around her. Because she is not changing, she is viewed as odd or strange. I do not think there is anything eccentric about her actions or reactions...she is merely doing what she is used to doing.
Miss Emily isn't eccentric as much as society and the times have changed and she has not. Just as a grandchild may not understand the reasons for the grandparent's actions, it does not make the grandparent eccentric. The same is true of two people from different cultures. Miss Emily's ways are not the norm anymore...the folks for whom her actions are the norm have all passed away, just as the way the town operates and the land surrounding the once-noble and aristocratic home where Emily lives have also gone by the wayside.
While the reader must remember that "A Rose for Emily" is told from the point of view of a narrator who is one of the townspeople, not one of the old Southern aristocrats that Emily is, Emily's behavior is perceived as extremely odd. Nevertheless, Emily, like Miss Havisham of Charles Dickens's "Great Expectations" acts beyond the mores of her social class as her cousins--like the Havisham relatives--disapprove of her behavior and visit her to convince her to be rid of the Northern lower class man.
Certainly, Emily's attempt to keep her lover by poisoning him with arsenic reminds the reader of the eccentric aunts in the play "Arsenic and Old Lace" who poison their visitors to keep them from being lonely. In this play, the nephew, upon learning about their actions, is appalled at such eccentricities. Like the aunts, it is Emily's inability to adjust to the modern world that precipitates her actions; in her mind she must maintain her social status by believing in the world of her father. This refusal to accept reality is definitely an eccentricity.
In "A Rose For Emily", the main character is not eccentric. Every action that Miss Emily takes is done with clear thinking. After years of being under the control of her father, Miss Emily's action's, though eccentric to the reader are her way of gaining control in her own life.