Question

Which country was the titanic closest to when it sank

Answer 1

The Titanic was close to North Atlantic some miles away from south  Newfoundland, Canada when it sank. 

Answer 2

Titanic sunk in the Atlantic Ocean in the early morning hours of 15 April 1912.
Four days later the ship hit an iceberg about 1,000 miles from its planned destination point in New York. It sunk about 400 miles from Newfoundland, Canada.

In 1912, the Dominion of Newfoundlad was an independent country and part of the British Empire, but not part of Canada or Great Britain. It became part of Canada in 1949.
 
So, the correct answer, I think it is The Dominion of Newfoundland