Ok. So what type of food and what price range?
We got one of the finest Russian restaurants in the World called Saslik, I've been there twice and like that place. It's freguented by diplomats, situated in area with embassies and there's few troubadours singing & playing russian folk songs (most nights). You can have caviar, bear or reindeer.
http://194.100.211.168/saslik/index_e.asp
Now, here I have never been. First ever Finnish restaurant to get Michelin's **. That kinda shows in the prices, but I am truely curious about the place.
http://www.chezdominique.fi/
Then there's restaurant called Lappi (Lapland). They also got caviar & reindeer etc. but the food is a bit cheaper. I haven't been there, friends who've been there with foreigners said it's good, but Saslik is the favorite.
http://www.lappires.com/
Zetor is named after a tractor company. Prices are decent and this is laid back place. Review from one website: "A positively unique interior complete with tractors, shovels, milk cans from the Finnish countryside; there is even a sauna! In a way the restaurant is a joke, but the food is good and prices reasonable. In the evenings the place looks more like a barn dance, but in the rock spirit."
http://www.ravintolazetor.fi/eng/index.html
These are the places for local "Experiences", or then there's Japanese/Italian/TexMex/whatever, but those you can get back home too.