This question has already been asked and answered here on eNotes. Here is a link for you: http://www.enotes.com/dubliners/q-and-a/what-symbols-used-araby-by-james-joyce-70803
Let us remember that symbols do not necessarily need to be objects, they can also be characters or actions. You might want to reflect upon the symbolism that the boy sees in this story based on how he views Mangan's sister and also the journey to the bazaar that she sends him on. Part of the richness of this story comes from the way that the boy is presented as suffering from romantic illusions, and this is strongly suggested in his description of how the thought of Mangan's sister occupied his thoughts and hours during the day, even at places that are normally "hostile to romance" such as the marketplace. Note what the narrator tells us of how his thoughts are obsessed with Mangan's sister:
I imagined that I bore my chalice safely through a throng of foes. Her name sprang to my lips at moments in strange prayers and praises which I myself did not understand. My eyes were often full of tears (I could not tell why) and at times a flood from my heart seemed to pour itself out into my bosom... But my body was like a harp and her words and gestures were like fingers running upon wires.
Symbolically, then, we can see that the impressionable narrator regards his relationship with Mangan's sister much as an Arthurian knight's relationship with his love. He imagines being sent on a quest by her, much as Galahad had to retrieve the Holy Grail, and the simile comparing himself to a harp at her touch indicates the total control that she had over him. Symbolically, from the narrator's point of view, the "quest" that Mangan's sister gives him thus has a much deeper significance, as it gives him the opportunity to show and prove the steadfastness and the purity of his love.
In additition, you might like to consider the symbolism of the bazaar itself, especially as suggested by the final paragraphs, and how the symbolism that the boy gives the events in this story is replaced by a deeper and bleaker symbolism at the ending. Good luck!