If you want to try something really local and special in Helsinki, you should definitely spend an evening at Elite, founded as early as in 1932. Many famous Finnish singers, writers, painters, actors have considered this almost their own living room.
Even today you can hear interesting stories about their regular tables and orders. The menu in Elite is traditionally Finnish. You might even run into a big party (with dancing, drinking and eating) after the moose-hunting season! The restaurant is closed on Sundays but you can still make reservations for bigger groups for that day.