Terve,
I used to live in Turku in Finland and maybe I can give you some ideas.
Helsinki is definitly worth a visit, but to be honest what makes Finland special is the countryside. So do not waste too much time in Helsinki or Turku. The southern coast is nice towards the west, where you can hop from island to island. Otherwise, I can recommend the large lakes in the centre of Finland. Lahti to Jyväskylä is definitly worth a trip.
Basically most of the country's population lives in the southern third. So that is where the population is dense for Nordic standards. But once you get out of the Helsinki-Espoo metropolitan area, it gets very provinvial (thats where Finland is best).

Cost: slightly expensive on food, but as a bike traveller, your other costs should not be too bad.