Any physical item can serve as a symbol in a great literary work, since great authors choose those details that reflect and resonate with the whole of the work. So keep in mind the global question of why Joyce is even telling us this story, why it matters, and that focus will allow the symbols rise to the surface. Why does this story of a boy and his desire matter to readers today?
A question that is good to ask is, How much is it a symbol versus a functional object? We can get carried away by seeing too much meaning in tiny details. But those that get mentioned often or that are rendered with powerful description -- those objects we should spend our time on analyzing. Objects can be functional. For example, the florin in the boy's pocket is a means to get him into Araby, the bazaar. On a symbolic level, what does money really mean in this boy's life? How much wealth does this boy have to begin with? Answer that, and then the florin takes on a new significance: it represents an idea of povery, wealth, or aspirations.
The florin is functional in another way, by enabling him to get inside Araby and buy...what? (Now remember Mangan's sister and what the protagonist thinks of her.) What is his goal once he's inside Araby? Here is a second, symbolic significance to the florin: the emotion and desire it represents. You will need to search earlier paragraphs where the boy is practically trembling with emotion, if you need to pull evidence for his feelings, and then attach it to the mission he's on while at Araby.
The home where the boy lives has symbolic potential as well. Note who once lived and died there. What are the first things you think of when you think of a priest? Explore those connotations. An example: the first thing I think of when I see the color red is love, hearts, Valentine's, blood, etc. So, if you think of the priesthood, what words come to mind? Brainstorm a long list of associations, then circle the ones that might have some relation to a boy who is lovesick for a girl he barely knows. There's your significance, or symbolism: the themes that the image of priesthood raises. Remember that Joyce did not have to give the history of this house, that it was once occupied by a priest, nor mention it a second time. This setting is symbolic in a number of ways, but homing in on the home's prior occupant will lead you down a thematic path with some rewards.
Araby itself, the place the boy hopes to visit to achieve his mission, has symbolic potential. What will going to this place achieve for the boy? Why might it be called Araby? (Note that the uncle asks his nephew if he knows the poem, "The Arab's Farwell to His Steed," a ballad about an Arab who sells his favorite horse and then in a fit of regret, tosses away the money he gets for the horse and takes the horse back.) What does Arab culture represent to these Irishmen? To this Irish boy in particular? And how, like the priesthood, might you connect Arab culture (or the Irish stereotype of it) to this boy's infatuation with Mangan's sister?
Money, house, and bazaar: this object and two elements of setting can help you in probing the symbols of the story. Remember, symbols are vehicles of the story's larger idea.