How does living on a certain side of a mountain range often create different climates and what cities encounter these changes?
A mountain range can sometimes produce separate types of climates on either of its sides, depending on other meteorological conditions and factors. A mountain range can sometimes trap moisture on one side of its range while effectively blocking that moisture from reaching the other side. This phenomenon is called rain shadow. One excellent example of this are the Cascade Mountains in Washington and Oregon in the US. Moist air and clouds moving inland from the Pacific Ocean provide plenty of rainfall to the western parts of these states, including cities like Seattle, Washington. Seattle has a reputation for being very rainy but it actually doesn't receive any more rain that several other major cities in the US. But it does receive plenty of atmospheric moisture and clouds from the ocean that get blocked by the Cascades from moving away from the area quickly. The moist air from the ocean hits the mountains and this causes the air to cool and lose its moisture in the form of precipitation. In fact, parts of the western Cascades are some of the wettest places in the US with sometimes record breaking snowfall.
On the other side of the Cascades is northern Idaho and the city of Coeur d'Alene. This eastern expanse from the mountains is much drier than the ocean facing side and parts of it are considered arid. The trees and forests are also more sparse than on the western side. If you ever drive through the area from west to east you will definitely notice the change when you cross the mountains.