This website says that the last home of Mary, the mother of Jesus, was in Ephesus, Turkey.
Where did this idea originate?
Here is a Wikipedia article (poor resource sometimes, I know) that details the origin of the story that Mary lived in Ephesus (or nearby).
It appears to start with a nun in Germany named Anne Catherine Emmerich, who was bedridden and reported a series of visions that detailed "the last days of the life of Jesus, and details of the life of Mary, his mother." She had a visitor, who was an author named Clemens Brentano, who transcribed her visions and later after her death published a book about them. In one of his accounts was a description of a house that John built for Mary in Ephesus, which provided details of the area:
In 1881 a French priest, the Abbé Julien Gouyet, found the house by using the notes in Brentano's transcripts. The rest, as cheesy as it may sound, is history.