Hakaniemen Market Hall has been operating since 1914, so they know what they are doing and it shows. This is the closest Market Hall in the city from my place and I think it is the most useful for everyday shopping.
It is not as pretty as the Hietalahti Market Hall, but then generally all things are more rough-around-the-edges this side of the bridge, which is not necessarily a bad thing. They are also more concentrated on groceries, although there are restaurants as well. So, if you are looking for fresh fish, meat, bread, vegetables and mushrooms, delicatessen, cheese etc. this is the place for you. On the second floor they have speciality shops that sell design, wooden toys, clothes and gift items, which can make very special souvenirs.
The Hakaniemen Market Square in front of the hall operates until 15:00 (except Sundays) when the weather is not horribly cold and they sometimes have special market days, so you can find some vendors outside as well. (Summer) morning coffee on the square followed by shopping in hall, is a Helsinki classic! My favorite coffee tent is run by Kahvisiskot, with their steaming coffee, great “pulla” and even pancakes, they are to be found at the square again from March on.