There are four places total, but Moscow is in two separate scenes. The first setting is Yalta, where they first meet. This is where their love began. Together they go to Oreanda. This is significant because it was so quiet and peaceful for them. Everything was beautiful there to them: "The sea, mountains, clouds, the open sky." When they see how late it's getting, they head back to Yalta. Here they must part ways and go back to their spouses. Dmitri goes to Moscow, and Anna goes to a town unnamed (S----).
After spending months apart, he heads to her town to find her. There they meet briefly, but with her husband there, she refuses to spend time with him and promises to come to Moscow to see him. This is significant because she cannot be untruthful in her home town, yet she'll go to his town and do just that. In this last scene in the story, they confess their unending love and decide to work out something so they can remain together (while still married to another).