When we were in Gdansk, Poland in December 2012, we took a, very cheap, train to Sopot which is a summer beach resort and was very closed for the off season. It was also very cold! -10 degrees C, which is as cold as this delicate flower has ever been! In Sopot you can walk out on the longest pier in Europe which takes you out into the Baltic Sea.
Just a little note on Gdansk, it’s cheap! Compared to the UK, Poland is quite cheap (although I imagine places like Warsaw get a bit more pricey), and you can get food and drink for not very much money so we all had a cocktail or two.
I would recommend Gdansk for a few days, we went for a long weekend, but not much longer. The old town was very picturesque and Christmassy and it was fun to experience the extreme cold temperature as well. But after a few days I think you would easily run out of things to do.