On Thursday is the birthday of Helsinki that was grounded in 1550. The whole programme is here: http://www.helsinkipaiva.fi/en/all-programme. Among other things, there will be an outdoor concert near the Paasitorni: http://www.helsinkipaiva.fi/en/radio-aalto-helsinki-day-concert. But considering the weather, perhaps the free entrance to the Ateneum Art Museum: http://www.helsinkipaiva.fi/en/free-admission-ateneum-helsinki-day-tove-jansson-exhibition.