We read online that the Ateljee Bar in the Torni Hotel has the best views in Helsinki. We found it on the map - and went their for a drink after dinner. It didn't disappoint... the views were so pretty, especially over the Baltic. You ride in a tiny elevator to get up there, and then go up a windy staircase, but it's worth it.
We went here on our last night and it was neat to see the city we were exploring from up high.