I had to do a little research to answer this one since I know far more about the 19th century and post-1952 relations than I do about the 1920s.

Calvin Coolidge, who historian Lars Schoultz refers to as the "only sitting president to ever visit Cuba" (pages 30-31 of the 2009 First Edition), arrived in the context of the Pan American Congress then taking place in Havana, Cuba. At the time Gerardo Machado was the elected leader of the country but had already begun a series of repressive policies against dissidents which were to lead to him earning the nickname of "the butcher of Las Villas" (Las Villas being his hometown). He was a faithful tool of US interests and American representatives wrote back to Washington frequently with contented missives about how he was being supportive of just about any issue they brought up.

This was also in the context of Cuba still being subjected to the Platt Amendment (an imposed amendment to the Cuban constitution allowing US intervention whenever, wherever, and for however long the US saw fit, if Washington thought it necessary). That would be the first problem tackled by the post-Machado Revolutionary government that overthrew him in 1933 in the midst of a bloodbath of revenge killings against Machado´s supporters who failed to escape. When Revolutionary president Grau San Martin was offered the Cuban constitution in 1933 he refused to swear on it before taking office because of the Platt amendment (he was overthrown and a new constitution wasn´t implemented until 1940).

An interesting article was just published in The Atlantic today pointing to the 1928 Pan American congress in Havana as a key point in the rearticulation of US policy towards the region, but I am having difficulty confirming that. Maybe flairs more expert in the period than I can confirm this. I seem to recall Tulio Halperin´s book on the Contemporary History of Latin America, published in the US by Duke University Press, talking about this point but I don´t have my copy at hand and thus won´t speculate on the issue.

It is telling that the visit, whatever transcendence it had for America´s broader Latin American policy, is mentioned only in passing by Schoultz and not at all by Louis Perez Jr., whose Cuba and the United States: Ties of Singular Intimacy doesn´t even bother to include Coolidge in the book´s index or mention the visit in the pertinent section on that period.

Lars Schoultz: That Infernal Little Cuban Republic.

Louis Perez Jr.: Cuba and the United States: Ties of Singular Intimacy

"The Last Time a US President Visited Cuba" by Krishnadev Calamur in The Atlantic, 02-18-2016: http://www.theatlantic.com/international/archive/2016/02/cuba-obama-visit-colidge/463356/