If you are into design and handcrafted things, consider taking a guided tour of the Arabia factory. There is an outlet store in the building that carries a selection of Finnish design goods. You can find great deals on some of the items. The tram 6 will take you here from the city center.
An unique cafe that is definitely worth the trek. You'll want to spend time relaxing in the hammock or on the bean bags and admiring the city skyline. Make sure the weather is nice, the cafe might be closed if it's rainy. The whole Kalasatama area is very interesting. You can skate, create graffiti art, or tend your urban garden here. Easily accessible by the eastbound Metro. (The stop is called Kalasatama.)
The Hietaniemi cemetery is an interesting place to explore. It's especially pretty during the winter when it's dark and you can see the candles left on the graves. Many influential people have been buried here, and the cemetery has beautiful memorial sites for soldiers who fought in the wars.
A charming flower shop and a cafe. The setting is perfect for an afternoon of catching up with a friend and sipping delicious coffee. This is not a place for a quick caffeine fix - you'll want to stay for a while and enjoy the cozy, relaxing atmosphere. They also serve raw cakes and brunch. A must when visiting Helsinki.