It’s pretty simple. Los Angeles is a patchwork of ethnic neighborhoods, all of whom specialize in their particular fare. So when in doubt, try to go there for your grub. It’s almost always worth the effort.
If you want Chinese Food, with some exceptions, go down to Monterey Park or San Gabriel or Alhambra. If you want real Mexican-Mexican Food, and not Tex-Mex which you can get anywhere, try Boyle Heights. Go to Thai-Town, Little Toyko, Koreatown, Little Armenia, the Byzantine-Latino Quarter (for Greek food), Little Russia. Don’t fret none. Your money’s still good there. You’re as capable at pointing at what you want on a menu as anyone else. It’s a perfectly legitimate form of communication.
And more importantly, don’t be afraid to ask a native.