American interest in hawaii, china, cuba and other locations around the world originated because?

The historical precedence of isolationism as a form of government policy began in during the time of the Revolutionary War, the latter part of the 18th century, due to the fact that the colonies respected the ideals of autonomy and self-reliance. The colonists had revolted against Britain to attain their independence and through their sufferings as colony, recognized that Britain's imperialism and the idea of imperialism was something to be avoided. Thus began the government policy of isolationism, or attempting to minimize international relations unless for clear purpose of trade that would not expose the government to more responsibility or difficulty like an imperial power.

However, this policy could not last, as the increase in technology in transportation and communication continued to make the world a smaller place with diplomatic relations and commercial interests increasing on a global scale. Some of these ideas of technology include the innovation of the telegraph and improved sailing technology to better and more safely transport people and goods across the oceans.

One of the most dramatic shifts in the this policy of isolationism to expansionism occurred at the end of the 19th century with places like Hawaii and Cuba. Due to the location of Hawaii it was much more likely to be influenced by China and indeed in the agricultural industries which flourished in Hawaii, attracted significant numbers of Asian workers, including many Chinese. So at the end of the century the U.S. saw that it would be beneficial to maintain some improved relations with Hawaii as a strategic gateway to Asia via the Pacific routes and therefore moved ahead with normalizing relations with Hawaii and designating it a form of protectorate in order to maintain the business relations that had been developed there. 

Cuba along with several other Latin American countries/colonies, on the other hand, were becoming more and more influenced by the Spanish. The U.S. government did not like another strong foreign imperialist country beign so close to the U.S. homeland. In 1898, the U.S. worked to secure independence for Cuba and other nations.

So the interest in these places came about in order to protect U.S. interests in business and government. The U.S. tried to maintain policies of isolationism into the 20th century, but business and diplomatic relationships along with the two World Wars would forever change this and eventually result in the U.S.'s status as world superpower/leader/imperialist.