It depends. When referring to a specific region, you should capitalize the words West Coast such as “I’m traveling to the West Coast” since “West Coast” is a proper noun in this case.
However, if you are referring to a general region, such as “the west coast of the United States” then you should keep the words lowercase.
Confusing, we know, but the capitalization rules for west coast are related to why directions are also sometimes capitalized and sometimes not. You can read more about the rules for directions here.