Seductive and secretive, Cuba has captured the imagination of American travelers for decades—not least because it has been shrouded in mystery for so long. The birthplace of salsa and producer of coveted Cuban cigars, it is a small country that has made a large splash around the globe both culturally and politically. For years, Cuba was closed off to American tourists. And though people still found ways to visit the country illegally via Mexico or Canada, Cuba managed to avoid the levels of mass tourism found elsewhere in the Caribbean.…