What is the narrator's age in "Araby" when telling the story?

We are not told the exact age of the boy who narrates "Araby," but the story indicates he is at the cusp of a transition from boyhood to adolescence. He goes to school, he plays games with the other boys in the streets until dark, and he is under the thumb of his aunt and uncle. He cannot go to the bazaar called Araby if his uncle doesn't take him.

We know he is more than just a little boy because of his awakening sexual desire, which he focuses on his friend Mangan's older sister. As he puts it:

Her dress swung as she moved her body, and the soft rope of her hair tossed from side to side. 

He watches her from afar, and she becomes an idealized object of his desire. She doesn't have a name that we are told, but he conflates her with the Virgin Mary, symbol of motherhood and purity, and with the exotic bazaar Araby, symbolizing the mystery and sexuality of the Orient. As he views her one day, the word "white" stands in for the mixture of purity and sexuality she represents to him:

The light from the lamp opposite our door caught the white curve of her neck, lit up her hair that rested there and, falling, lit up the hand upon the railing. It fell over one side of her dress and caught the white border of a petticoat, just visible as she stood at ease. 

When she speaks to him of the bazaar:

The syllables of the word Araby were called to me through the silence in which my soul luxuriated and cast an Eastern enchantment over me. 

Yet like a young adolescent, his emotions are in turmoil, on a roller coaster ride, and quickly crash into disillusion as the bazaar—and thus the girl—don't live up to his expectations. Like many young adolescents, he is sorting out fantasy and reality as he gropes to come to self understanding:

Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger. 

What is the narrator's age in "Araby" when telling the story?

James Joyce's The Dubliners, which he wrote as a "stages of man," has three stories devoted to the following stages:

1. childhood
2. adolescence
3. mature life
4. public life
5. married life, which is inserted between adolescence and mature life.

"Araby" falls into the adolescent stage, a stage in which the teen characters are all failures.  In the first paragraph of this story, the narrator describes North Richmond Street, which is quiet until the Christian Brothers' School sets the "boys free."  As he continues his description of his neighborhood, the narrator describes his play with the other boys; they shout and play "till our bodies glowed." Mangan's sister, for whom the narrator has an imaginative infatuation calls her brother in for "his tea."  Later, when she speaks to the narrator, he remarks,

When she addressed the first words to me I was so confused that I did not know what to answer.

The narrator's  immaturity is clearly indicated by his play and his confusion when he does talk to Mangan's sister, and it is suggested by the romanticized concept of love that he constructs as the Arthurian knight pursuring "the grail," as well as his burgeoning sexual feelings as he lies on the floor in the front parlour where he peeks through the blind, watching her.  These indications, therefore, point to the narrator as a boy in the early stages of adolescence.

What is the narrator's age in "Araby" when telling the story?

The narrative point of view of this story is actually first person objective, and this means that the narrator is a participant in the story but that he is narrating it after the events have taken place.  You can typically identify this point of view by noting that the speaker uses the first person pronoun "I" and past tense verbs when narrating the story's action.  So, the narrator is actually an older person who is looking back and telling the story of what happened to him many years ago (his word choice in certain parts of the story alert us to the fact that he is much older now).  However, when the story's events were actually taking place, the narrator was of an age when he played outside with all his friends: running and hiding and pretending together.  This is a good clue that the narrator is perhaps in the 8-10 year old range. 

Is the narrator of "Araby" young or mature at the time of the story?

When the narrator tells this story, he seems to be an adult looking back on a childhood experience. He is a first-person objective narrator, one who is a participant in the events of the story and who tells it after these events have already taken place. The verbs in the past tense are a good clue. Although we cannot know exactly how old the narrator is now, his word choices and analysis of the events he experienced as a child make it seem as though he is well into adulthood. He describes the "career of [their] play" as children and running the "gauntlet of the rough tribes" from cottages to gardens. He describes the name of Mangan's sister as being "like a summons to all [his] foolish blood." Such descriptions are not likely to come out of a very young mouth, but, rather, that of an adult who has had some time to process and reflect on his experiences. Further, the final sentence, which describes his epiphany, is very mature: "Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger." Again, these types of word choices seem to mark the narrator as a person well-advanced into adulthood, reflecting on his loss of innocence as a child.

Is the narrator of "Araby" young or mature at the time of the story?

This is an interesting question to consider. Firstly, let us note that the story is told in the first person, by the boy himself who experiences such a significant epiphany in his adolescence. In addition, let us also be aware that the story is told in the past tense:

On Saturday morning I reminded my uncle that I wished to go to the bazaar in the evening.

Note the use of the first person in "I reminded" and also the past tense in "reminded" and "wished."

Therefore it is clear that the narrator is looking back on his youthful past as he tells this story. However, what we are not told is how old the narrator is as he tells this story. We can perhaps infer that he is telling this story in his later years, because we can guess that anybody would have needed a significant amount of time to process such an experience and its importance, and what he could have learnt from it. However, no clear indication is given in the story.

What effect does the age difference between the narrator-as-character and narrator-as-storyteller produce in "Araby"?

Because the narrator now seems to be a grown man who is reflecting back on his childhood experience of his first love, he is able to provide us with impressions and information that a young boy would not necessarily have thought to do, especially if he were narrating events as they were happening. A young child narrating events as they are happening would not likely be a very reliable narrator; as a result of this older narrator's experience and maturity, however, he is likely a great deal more reliable. He has had time to reflect on these events, to consider and interpret them, and this means that he can present only the details that are truly meaningful and significant to the story. Further, the narrator's final realization—that he was "a creature driven and derided by vanity"—is not likely how he would have presented his epiphany when he was a young boy: clearly, the child realized something significant, but the man is much more capable of conveying what this epiphany is, and this helps readers to understand it more fully.

What effect does the age difference between the narrator-as-character and narrator-as-storyteller produce in "Araby"?

Often in this structure, the mature voice of the narrator comments on the action as it occurs; an example of this is the narrative device in To Kill a Mockingbird, where the older Scout constantly interprets events for us as the younger Scout enacts them.  In "Araby," the narrator does not interpret as the story proceeds. He recounts the events compassionately, but never saying as the story develops something such as "I was a romantic fool, young and innocent, not knowing the ways of the world," which is what we understand by the end of the story.  Indeed, even at the end of the story he does not explain and interpret but again "shows" (rather than "tell"s and reflects upon) what the character learns:  his eyes "burned with anguish." This strategy of "showing"  heightens drama and preserves complexity, too, for the narrator has a more demanding responsibilit to relate events through symbols and motifs--these carry a great weight in understanding "Araby."