The movie takes place in and around the city of Krakow, Poland and the nearby territory: mostly in the Jewish ghetto set up after the Nazis conquered the country, and the Plaszow labor camp set up outside of Krakow. Spielberg set the film here because… well, because that's where the events took place.
Poland sat at the very heart of the Holocaust and suffered the most grievous casualties. Before the war, about 3.3 million Jews lived in Poland. Three million of them were killed in the camps: half of those killed in all of Europe. There were six extermination camps and other forced labor and internment camps in occupied Poland.
Anti-Semitism ran extremely high even before the war, even though there were thousands of Poles who hid and protected their Jewish neighbors. The Nazis didn't act alone; they were aided by Poles who hated Jews just as much as they did and were more than happy to help (source). The Nazis had collaborators in every country they conquered; Poland was singled out simply because it had the most Jews. Ninety percent of Poland's Jewish population was killed in the Holocaust—the most not only in numbers, but also in ratio.
Most of the film was shot in the vicinity of Krakow: as close to the real thing as Spielberg could get (source). In cases where the buildings still existed, like Schindler's enamelware factory, he shot there. In cases where they didn't, he built new sets, sometimes from the original blueprints. The only exception was Auschwitz itself. The director shot only outside the gates of the camp, then built a set for the scenes inside the camp.
One of the locations shot outside of Poland was the Jewish cemetery where the real Schindler is buried: The Mount Zion Catholic Cemetery in Jerusalem.