Using 2-step authentication
You can't log in to Google services without your password. What you can do however is activate 2-step verification:
2-step verification requires two independent factors for authentication, much like you might see on your banking website: your password, plus a code obtained using your phone.
It's an extra step, but it's one that significantly improves the security of your Google Account because it requires the powerful combination of both something you know—your username and password—and something that only you should have—your phone. A hacker would need access to both of these factors to gain access to your account.
If someone might get hold of your password, they'd have no means of accessing your Google Account other than with your phone as well.
Here's Google's own Help page for 2-step verification including a video.
Using passwords that you can revoke
With the 2-step verification there comes a problem: Some applications still rely on the "user/password" scheme and need one single password to login.
You can generate application-specific passwords under My Account. Those are passwords you can enter instead of your normal Google password. They will work as expected, but don't require you to use the 2-step auth.
In your scenario, you could create an application-specific password for a public computer, enter it there, and as soon as you're home, revoke it. That way – even if there were a keylogger – the obtained password would become useless after revoking.
Another solution would be to carry a USB stick with a KeePass database. This database would have your Google credentials, but it would be secured by some other password.
In the public place, just
- plug in the USB stick
- open KeePass portable
- open the database file
- and then enter your KeePass password (possibly with another additional lock file that is needed to open the database. This file could be hidden as a
.doc file or anything.)
Even if there were Keyloggers, they wouldn't know where that KeePass password belongs. Then you can copy and paste the Google credentials to the Google Login page.
This is only safe assuming
- The clipboard isn't sniffed
- The USB stick contents are not copied to the computer without you knowing
Also, as @grawity mentions below,
KeePass has an "Auto-type" function for entering passwords automatically, which can be triggered by hotkey and is secure against keyloggers
You can find out more about Auto-Type on the KeePass website.