Either Yahoo or Gmail is perfectly fine.
For Yahoo, your only other two-factor authentication method is for them to send a notification to the Yahoo app on your phone. If you have wifi on your phone while overseas then that would work well for you. Yahoo doesn't offer offline code generation like Google does.
If you want to use a Gmail account, you can set up your phone before you leave with the Google Authenticator app, which once set up doesn't need any data connection. You just enter the six digit code it displays when Gmail asks for it.
Gmail also supports login approvals via the Google App on your phone, but that requires an active data connection, like with Yahoo.
I'm not sure why you'd be getting an error that your Google login can't be verified unless you're entering the wrong code. I've been using 2FA with Google for years and never had an issue.
If you enable 2FA on Google,
be sure to print out and save in a safe place the list of backup codes or you might never get back into your account.
Originally Posted by
TravelinSperry
Yes, but what if you lose your phone? You'll never get in.
I travel and do not need a code to get into Yahoo or Gmail. This can be turned off I'm sure (since I have never been asked for a code while traveling).
It's just a matter of time before a keylogger captures your password. I hope you use separate passwords for each account. You haven't been asked for a code because you have the feature turned off. As I mentioned above, Google will give you a list of backup codes you can use one time each to get in.