'West-coast' in rock is most often thought of as referring to laid back, sun and surf-inspired 1970's country-rock, think America, Eagles, Poco.....all dyed jeans and hawaiian shirts.
Twenty years earlier, however, jazz had a similar movement, also called the 'West-coast' sound, also relaxed: Cool jazz !
In the late 40's and early 50's be-bop was dominant; fast paced, aggressive music pioneered by 'the bird', Charie Parker. Cool jazz developed when artists from California went to New York and inspired by the cooler sound of sax-master Lester Young developed this 'West-coast' sound.
The Dave Brubeck Quartet are the perfect example of this type of jazz: the dissonance is smoothed out, the arrangements are important again, the chamber music of jazz
The most popular album is probably Birth of the Cool by Miles Davis (1957) but there is so much more to explore: here's some reccommendations
1. Paul Desmond Take Ten
2. Gerry Mulligan What is Tere to Say
3. Chet Baker and Art Pepper Playboys
4. Lennie Tristano Intuition
5. Art Pepper Meets the Rhythm Section