It turns out that DNA provides WLAN access in the guest harbour on Smultrongrundet. Sadly you cannot get access for one day or so but have to be a subscriber. The service is not cheap. The fee for flat rate is 90 euros per month. There are cheaper alternatives, but they are not flat rate.
Public WLAN doesn’t seem to be a big thing here in Finland. At least not affordable WLAN. Perhaps the good GPRS access slows down the WLAN expansion. Many WLAN operators offer GSM and GPRS access too. Maybe they don’t want to eat market share of their lucrative GPRS traffic (mine is over 2 euros per megabyte).