Design Forum Shop in downtown Helsinki is for sure a place to visit. Their shop gives a quick overview of Finnish design products. Products from the top dogs such as Harri Koskinen, Woodnotes and Marimekko as well as from the younger successfull designer brands such as Iivana Helsinki, ChoCho and Doctor Design.
In the same premises, there is a changing exhibition that can be visited for free. Their cafe is worth stopping by for it's good coffee but also for the quick peak to the local design publications.
If you have only time for one visit in Helsinki, this is the safest bet.
Design Forum Finland, Erottajankatu 7, 00130 Helsinki, Tel. +358 (0)9 6220 8130
Open 10AM - 7PM on weekdays and 12AM to 6PM on weekends.