We can not be certain where Jairus lived.
In Luke 7:1, Jesus enters Capernaum, and the next day he goes to Nain (v11). Later on in Luke 8:22 he crosses the Sea of Galilee to the country of the Gadarenes (v26) and then later “returned”, which is where he meets Jairus (v40-41). So it is possible that Jairus was from Capernaum, where there was a synagogue (Luke 7:5) and where Jesus did a lot of preaching.
Having said this, it is not certain how much time separates the events of Luke 7 and 8. In fact, in Luke 8:1 it describes how Jesus went through “every city and village”. So whilst Capernaum is the strongest candidate for the home town of Jairus, the evidence is only circumstantial.