One thing I noticed while I was in Dublin this summer is that everything is incredibly compact--it really doesn't cover that large of an area. If this was the state of the city in 2014, I bet it was even more compact in Joyce's time. The neighborhood in Araby is no different from the rest of the city. Many of the main buildings that would have been important to families living on North Richmond Street were very short distances away from their homes. Though Joyce never explicity mentions a church in Araby it's a fair assumption that the people mentioned are practicing Catholics. After looking around on Google Maps for a bit, it seems likely that they would have been in the parish of St. Agatha. It's only 0.3 miles from the Araby house, and construction was completed on the church in 1908, making it a viable church for the people in the story. The same goes for St. Vincent's Girls School, the school probably attended by Mangan's sister. Since the boy goes to a school that is specifically for boys, I assumed that there had to be a Catholic girls school nearby. St. Vincent's is, approximately 0.25 miles from the Araby House. Adding further credence to my guess is the fact that a convent is attached to St. Vincent's, and Mangan's sister specifically mentions that she has a retreat at her convent during the weekend of Araby.
Between school, church, and playing in the streets, the children in Araby probably did not spend much time more than a half mile from their homes. This makes the boy's venture to the bazaar all the more notable. It is over 3 miles from his house--a true quest for someone who rarely gets more than a mile from home.