There are a couple of eastern Finnish specialities worth sampling:
Kalakukko
A type of large rye bread pastry with fish and meat stuffed inside, can be eaten warm or cold.
Lörtsy
A large, flat variant of the ubiquitous deep-fried meat pie lihapiirakka, can also be stuffed with apple jam
Vendace
muikku, a type of small freshwater herring, most commonly coated with rye flour, quickly fried and eaten while piping hot
Karjalanpiirakka
Karelian pie is a special kind of pastry made from rye flour and filled with rice porridge or mashed potatoes
The best place for eating any of these is at the market, found in the center of any larger town.