To be fair, the Bay of Pigs invasion was Eisenhower's brainchild. It's also worth noting that Fidel Castro did not declare himself a socialist before the invasion, and that only after it did he turn to the Soviet Union for aid, having already been ignored by Ike during a previous visit to Washington.
So if one really wanted to, one could trace much of the events of the Kennedy Administration to being caused by Eisenhower.
I list Ike as among the worst post FDR presidents, more or less tied with Reagan. Both are quite similar, though clearly not identical. Both of their administrations' foreign policies are largely based around intervening in the internal affairs of other nations, often as part of a strange paranoia about communists, socialists, and anyone to the left of Milton Friedman. In this regard, it is fair to also throw Nixon into the mix, for his opposition to Salvador Allende and Indira Gandhi, though the latter he did not help depose. Guatemala, Grenada, Nicaragua, Cuba, Vietnam, Iran: in all of these nations, leftist governments came to power, and were either actively engaged by the US military and most often deposed, neglected and forced to turn to the Soviet Union for aid, losing us another friend, and, in the cases of Iran, Vietnam, and Cuba, neglected the nationalist overtones of the revolutions, instead blindly screaming "REDS!" and charging into battle. In this way, Truman can also be thrown into the mix, for his careful negligence of Ho Chi Minh in 1945 that sowed the seeds of the Vietnam War.
Because the postwar policy of the United States has been one of intervention, hardly any postwar presidents are worthy of being noted as "great." Perhaps Kennedy does then deserve to be regarded as one of the best, as the few interventions during his short tenure were largely precipiated by his predecessor. In a similar way, perhaps Ford and Carter are also worthy of greater respect, not because of things they did, but beacuse of things they did not do. Don't misunderstand me, I am not totally against foreign intervention, but I am against ignorant invervention. Just as Clinton went to war in 1999 to protect Kosovar terrorists, and Bush in 2003 sent us into a land of which whose internal politics we were largely ignorant, so did the other men mentioned above, into politics which were neither our business nor which were properly understood. It is perhaps fair then to rank George H. W. Bush above the rest, then, for his foreign engagement, the Second Gulf War (Operation Desert Storm), was far different: it was not merely an American expedition, but an international one, with specific objectives and, when completed, our boys came home. The Kuwaiti expedition represented what America did once upon a time: liberator of the oppressed, but respecter of self-determination. No government was installed in Kuwait as we left, it was merely freed from Iraqi control. In context with the above, I rank George H. W. Bush as the best post-FDR president. To define the worst seems almost futile, though it is most certainly either Eisenhower or Reagan.