Hop on Hop off ferry did not work out well - they go clock wise and only anticlock wise once an hour, if that. We wanted to go to the Vasa Museum first (very interesting but half an hour or so is enough) as it was the furthest away, found we had to wait almost an hour for the next ferry to take us back to the centre. From here we walked into the Gamla Slan, which is like most old towns. Again, at the ferry terminal we were told the wait would be a while and then the ride would take close to 45 minutes - walked back to the ship which was 25 minutes in total.
The 7 eleven in the old city has internet, could not find any other spots.