The correct answer is option 2, the Sargasso Sea. The Sargasso Sea is a unique region in the Atlantic Ocean characterized by free-floating seaweed called Sargassum. Unlike other seas, the Sargasso Sea does not have any coastlines or land boundaries.

Option 1, the North Sea, is a marginal sea of the Atlantic Ocean that is bounded by several countries including the United Kingdom, Norway, Denmark, and the Netherlands, so it does have a coastline.

Option 3, the Baltic Sea, is a brackish marginal sea of the Atlantic Ocean that is located in Northern Europe and is bordered by several countries including Sweden, Finland, Russia, Estonia, Latvia, Lithuania, Poland, Germany, and Denmark, so it does have a coastline.

Option 4, the Bering Sea, is a marginal sea of the Pacific Ocean that is situated between Alaska to the east and Russia`s Siberian coast to the west, so it does have a coastline.

Therefore, the Sargasso Sea is the only option among the given choices that does not have a coastline, making it a sea without a coastline.