Usually people just think of mosques when they think of Iran. True, the majority of people in Iran are Muslim, but there are also Christians and Jews, and therefore also a number churches and synagogues.
Once such church that I visited was St. Gregory Stepanos, an orthodox Armenian church located in the ancient city of Ecbatana (or Hegmataneh) in Hamedan. In addition to the excavation sites in this area, there is a museum and this simple, yet lovely, church. It's quite a large area, so be prepared to walk, but a must-see should you visit Hamedan.