Wikipedia says the city is in present day northeast Ukraine.

And I'd like to add asking did these events spur mass immigration to the United States like the movie depicts the mice of the area are doing? Or any sort of mass Jewish immigration?

And is it related to spurring mass immigration from wider Europe because there is some sort of related worldwide historical event going on? An Italian mouse is on the ship when the main characters immigrate to America.

From wikipedia-

In Shostka, Russia, in the winter of 1885, the Mousekewitzes, a Russian-Jewish family of mice who live with a human family named Moskowitz, are having a celebration of Hanukkah where Papa gives his hat to his 7-year-old son, Fievel, and tells him about the United States, a country in which he believes there are no cats. The celebration is interrupted when a battery of Cossacks ride through the village square in an anti-Jewish arson attack and their cats attack the village mice. Because of this, the Moskowitz home, along with that of the Mousekewitzes, is destroyed, while Fievel has a narrow escape from the cats. They flee the village in search of a better life.