What was JFK's greatest success?
While there are many possible answers to this question since it is an opinion question, I would suggest that the handling of the Cuban Missile Crisis was President Kennedy’s greatest success. The Cuban Missile Crisis had the potential to lead to nuclear war.
When the Soviet Union began to build missile sites in Cuba and to place missiles with offensive capabilities in Cuba, President Kennedy had to respond. The security of the United States and the Americas was potentially at stake. President Kennedy was able to buy time by establishing the naval blockade around Cuba. The Soviet ships would take about ten days to reach Cuba. This gave us time to negotiate.
There were people who felt we should have gone to war over this issue. President Kennedy, wisely, chose a different path. Through negotiations, this crisis came to end peacefully with both the United States and the Soviet Union realizing they needed to prevent a situation like from happening again. Both countries realized we were too close to a possible nuclear confrontation. After the crisis ended, we signed an agreement with the Soviet Union banning the aboveground testing of nuclear weapons.
I would suggest that resolving the Cuban Missile Crisis peacefully was President Kennedy’s greatest success.