How Safe Is SSL In a Public Place (Airport/Coffee Shop)

Some, but there is risk everywhere.

Extra diligence is required, however, to ensure that your certificate is valid.

Never accept a self-signed or expired certificate in this scenario(you'll see security warnings from modern browsers). Click on the lock next to your URL to ensure everything looks good!

Ensure the the site is using complete SSL and not mixed mode(Some elements encrypted others not or login via HTTPS and pop back to HTTP after) and you should be alright to use it.