I deliberately trained myself to speak with a neutral American accent - probably what you mean by a West Coast accent - by watching particular actors and practicing - in private - speaking like them. In particular, for me, it was John Malkovich, who has perfect diction and enunciation.
This was in my teens and it took a couple of years, but it paid off. Nobody can tell where I'm from now, though people mostly assume California. I still say "y'all" but I say it with no Texan drawl, which sounds a bit odd to people, I think.
Just find people who speak the way you want to speak and watch them, listen to them, try to repeat things they say until you've got the accent down. At first it'll seem embarrassing, even if you're alone, and you'll find yourself feeling like a pretentious poseur for a while, but eventually you won't. It'll just be how you speak English.