This is a surprisingly hard question to find an answer for, but the best information I’ve been able to find seems to point to Cuba moving steadily westward as the Atlantic Ocean widens and South America pushes upwards towards North America, until eventually (some 250 million years from now) the continents reassemble themselves as Pangea Ultima and Cuba is sucked under what’s left of the Atlantic Ocean.
Then again, that may not have been the question the NYT had in mind…