Helsinki

[Springal]

Don't get the ferry to Tallinn, get the smaller boat. Much quicker and pleasant

 

[bristo]

Design Museum, 10 mins walk from centre, €10 closed Monday's in winter.
Reindeer meat as already suggested but have cloudberries for pudding (might be out of season though).

 

[hart's shirt]

 

[Cowfold Seagull]

Our tour guide said the Finns basically treat them as 'booze cruises'. They get pissed cheaply, eat in the restaurant and spend half the trip in the onboard casino before as you say stocking up on duty free.

Sounds just like the old 'booze cruises' across the English Channel back in the 1970/80's. They were really popular until the laws were changed, and it wasn't possible to buy duty free for trips within Europe.