How successful was American foreign policy towards Cuba during the 1960s?
It is hard to argue that American foreign policy towards Cuba was anything other than a failure in the 1960s.
In the early 1960s, the US adopted policies that ensured that it would have no influence over Fidel Castro. The US, worried about left-wing policies such as land reform, refused to give aid to Castro. This drove him into the arms of the Soviet Union. After that, the US was determined to get rid of Castro. The first attempt at this failed miserably at the Bay of Pigs. Economic and diplomatic efforts also failed to seriously harm Castro's regime.
The only possible success in this time period was the handling of the Cuban Missile Crisis. However, this had more to do with the Soviet Union than with policy towards Cuba. The bottom line is that the US lost all influence in Cuba and ended the 1960s with a hard-line communist state there that was completely hostile to the US. Therefore, we must conclude that US policy was a failure.