This is a must if you want to visit a real market square. The Kauppatori is touristic - this is more authentic with real market square cafees. Next to it there's the "Kauppahalli" market hall where you can buy everything from clothes to food. Many Finnish specialities available and excellent choice of meat and fish.
To be avoided: autumn-winter sundays when there's the "Maalaismarkkinat" market day. Only cheap rubbish on sale.