No HSBC on the island, there is a Barclays in Arrecife which I went to with a friend, only to find out their systems aren't linked to the UK so they are effectively a separate entity....
Personally I'd never login to Internet banking except from my own or a trusted computer. Definitely not from an Internet Cafe.
I absolutely agree with Alan on not logging on. Anytime you share a connection (even a secure one) anyone else could if they know what they are doing access you banking screen etc. You also should be aware that anywhere that has there own server (computer) can log the details you enter. Sorry don't mean to scare anyone but those are the facts.