not that.
You are not your address. You are your ability.
Get good enough and you can live in a wider array of cities. Be a hack and you may be limited to LA if you want to make your living doing audio.
This is not to say that LA is nothing but hacks (Its not - the best of the best tend to live there) It
is to say that there are a lot of hacks in LA.
Audio post production is an incredibly portable profession. Everything can be transferred via ftp. I live in Dallas and 60% of our clientele is not local to me.
I agree with the post above that said to do a short. Start there, don't start by moving.