With restored diplomatic relations with the U.S. and lifted travel restrictions, Cuba's landscape, culture and economy is changing – almost too fast for the time-capsuled country to catch up.

Since President Barack Obama announced that the U.S. would ease diplomatic relations with Cuba, the number of people looking to travel to the largest country in the Caribbean has steeply risen.

In December, New York resident Zachary Sanders agreed to pay $6,500 related to his 1998 visit to Cuba — after a long legal fight — but most Americans who get dinged pay about $1,000 ...