Where to find Google Authenticator backup codes?
You need backup codes to "an account" not to Authenticator itself.
Authenticator has one entry for each 2FA-enabled account of yourself - without needing an account for its own use. So the concept of backup codes for GA doesn't apply.
If for example, you have an account (say GMail) that you've protected with GA-based 2FA, then you could generate backup codes for GMail, from GMail Account Management / Security menus. Since the backup codes need to be recognized by GMail, they are generated in GMail - not GA.
Same logic applies for any other account that you need backup codes for.
Edit: To backup all the accounts you have on GA, you need to backup the "App-specific secret" (usually a long hex string; or a QR Code that has the string) for each account/app. AFAIK, GA doesn't use online storage to backup your GA-enabled accounts.
I agree with you that the "philosophy" behind Google Authenticator's "only one device" is profoundly broken, because in as much as it tries to avoid "copying" the keys, it exposes you to the risk of a broken device. Electronic devices can fail. You need a backup. Happily, Google Authenticator's keys can be extracted: http://eduncan911.com/technology/hardware/google-authenticator-databases-move-copy-fix.html