You can have porridge (the flavour depends on the day), coffee and pulla, sandwiches (I'd recommend the rye bread with gravlax), or, if your cardio-vascular system can take it, a deep-fried rice and meat pastry (lihapiirakka or "lihis"). Some of the places may also have quiche etc. Another typical Finnish delicacy available in some of the places is the Karelian pastry (karjalanpiirakka), which is best had with some egg butter. If you crave something sweet, munkkipossu (a rectangular, sugar-covered donut with apple jam filling). All quite delicious.

If you don't want to wander over to Hakaniemi, you can have most of the same stuff at the main market place. The only drawback is that the main market place is far more touristy. A further alternative is a small family bakery called Eromanga, which is located at Pohjoinen Makasiinikatu 6, quite close to the dead centre of town. Eromanga is famous for their meat pastries and their munkkipossus.

Cheers,
T.