According to Google Maps, Hamedan is about 470 KM from Shush, the Biblical town of Shushan.
If Mordechai and Esther lived in Shushan (where Esther served as Queen), why were they buried so far away in Hamedan?
The Persian Jews identify Hamadan with "Shushan ha-Bira," which obviously is a mistake.
An essay entitled "Esther’s Tomb Iran's Jewish queen defies decay and dissolution." by the Diarna Project offers an alternative explanation for the tradition that the tomb is in Hamadan:
Mount Alvand, which overlooks the city proper, hosted the summer residence of Persian royalty of the Achaemenid Empire (ca. 550?330 BCE, the period when the Purim story is believed to have happened). Tradition has it that Esther and Mordecai–after spending their final years at the royal resort–were buried in the city, next to one another, with a shrine constructed over their graves.
In addition, as noted in the Wikipedia article linked in the question, there's an alternative tradition that Mordechai and Esther are actually buried in the Galilee region of Israel.
They were buried on land owned by Esther which was given to her by the king. (Esther_8:7)
Haman was descended from Hammedatha of Hamedan.