Try to get out in the archipelago on a boat! Also a trip to the fortress island right outside of Helsinki could be good, boats leave from "Kauppatori" at the end of the Esplanadi street. Also just a walk through the city to the seaside in the south and a coffee at Café Carousel or Café Ursula.
All of this of course if the weather is nice... Otherwise the Kamppi shopping center and Stockmann are good for shopping. about 8 years ago