All the timelines I've seen with Nixon getting elected either have him become president in 1960 or 1968. But what would have to happen for Nixon to be elected president in 1964? Obviously the death of JFK would have to be gotten rid of or made earlier, since the timing of the assassination made it so no Republican could win in 1964 (probably why Nixon didn't run then in OTL).
For the first idea of Kennedy surviving, Nixon could probably capitalize on the Cuban Missile Crisis diverting Kennedy's attention from his campaign promises. The Republicans could claim that Nixon would have done a better job, and that Kennedy did nothing of value during his presidency. In fact, all he did do was bring the country extremely close to another Pearl Harbor.
For the second case, LBJ was a rather bad president and really only one because the memory of JFK was still fresh in the public mind and because the Republican alternative of Barry Goldwater was such a horrifying thought. I've been reading up on LBJ for a class on Watergate, and in 1964 a lot of people considered him untrustworthy, yet still voted for him because the idea of Goldwater was so much worse. If the Republicans had a less controversial nominee like Nixon, the landslide for LBJ certainly wouldn't have happened and the Republicans could have capitalized on LBJ's moral issues like they did in 1968.
So, taking those two ideas, what would the effects be on US and world history if Nixon was elected president in 1964? Would United States involvement in Vietnam still have escalated? Would there be better or worse relations with the Soviet Union? What about the Civil Rights movement?