There are two distinct settings in "The Lady with the Dog," by Chekhov: Moscow and Yalta. While things like Google Maps make it easy to figure out what these cities are like today, it is important to try and understand what these cities were like around the 1890's. "The Lady with the Dog" was published in 1899, and the turn of the century was a very specific time in Russian history.
Yalta was one of the most beautiful seaside spots in all of Russia, and it continues to be a popular destination today. I've attached a Pinterest link below that showcases a painting of the Yalta coast from 1890. While it is fairly simple, it provides an inside look into the simplicity and beauty that was felt by those who visited Yalta.
In regards to Moscow, I've attached a link that features postcards from the 1890's in Moscow. When you review them, you notice that Moscow is stunning. Even in dingy black & white and sepia, Moscow is towering and awesome. The roads are relatively free of congestion, and the powerful architecture takes center stage. Indeed, Moscow was one of the most beautiful cities in existence at the end of the 19th-century.
The first setting is the seaside spa in Yalta. The second setting is Moscow, when Gurov goes back home. Then he tells his wife that he must go to St. Petersburg on business, but he goes, instead, to Anna's hometown, which is unnamed.
The story then shifts back to Moscow, where Gurov finds his life difficult to live without Anna. The shifting setting is a backdrop for the affair that the main character has throughout the story. He must hide this illicit affair from his wife and family.
"Gurov has always taken women for granted and has treated them without compassion or respect. During the course of his affair with Anna, however, he becomes more and more concerned about the consequences of his actions."
"Chekhov's treatment of morality is complex; he is not conventionally moralistic, yet his story suggests a strong personal morality."
While we usually mean setting in terms of the physical details of the place in which the action occurs, remember that setting in literature incorporates much more than simple location. When literature is set in a particular place at a particular time, the setting also evokes what we might call atmosphere. Consider that the New York City of 1889 is quite different from the one of 2016, and a Friday in Central Park is quite different at 3:00pm and 3:00am. Setting is always especially important in Chekov.
There are two basic settings—i.e. physical locations—in this story, Yalta and Moscow. The places themselves could not be more different.
Yalta was (and still is) a seaside vacation spot where people go on carefree, sun and sand filled holidays in summer months with nothing in particular to do but seek after personal amusement, away from the daily routine. The setting, then, is perfectly suited to the idleness most closely associated with privilege, a place where people of means go to be both festive and bored.
Moscow, on the other hand, is a bustling city, frightfully cold in winter and dark and crowded with busy people—in other words, the complete opposite of Yalta.
Chekov chose the settings to be different in every conceivable way in order to emphasize and underscore the difference in the two sections of the story, from events to character development to mood.