I think all of your presumptions about Nixon's choices are dubious. He might be no worse than JFK on Civil Rights, possibly maybe better--or rather, he could make his own support look more activist while shrugging and apologizing he sadly can't get anything done because of Southern Democratic opposition--same old story going back to the Hayes administration. The difference between JFK and Nixon on civil rights would be Lyndon Johnson--with him on the team Kennedy had less plausible deniability and a certain degree of progress had to happen--then when LBJ was the POTUS, there just weren't any excuses left--given Johnson's personal commitment on the issue. So assuming we compare just Kennedy to Nixon--a bit of a push.
There would be no Cuban missile crisis not because of Vienna but because you assume, with some reason, that Nixon would be more aggressive than Kennedy against Castro. It seems odd you suppose he'd weasel out of 'Nam somehow but take a harder line on Castro, but let's just stick with Cuba for a moment. Basically he faces the exact same three choices, one of which was mindlessly off the table for both, Kennedy did. 1) Back off and accept Castro had taken over in Cuba and could not easily be ousted. That was unthinkable for either and they neglected it until it was forced on Kennedy by the outcome of the Missile Crisis OTL. 2) Go all in, commit to doing whatever it took to knock Castro out to hell with appearances. 3) find some sneaky, backdoor, cleverly plausibly deniable way to make the overthrow of Castro look like the will of the Cuban people, at least to American newspaper readers if not anyone else in the world. In fact Eisenhower initiated a version of 3), Nixon I suspect was rather deeply in the loop on it, and OTL Kennedy accepted it and green lighted it--we call it "the Bay of Pigs fiasco" these days. The whole premise was that Castro would be unpopular enough that these Cuban counterrevolutionaries we "secretly" backed would be popular enough, if not to win against Castro outright on the shoestring resources they had, to at any rate carve out a big enough base with enough visible popular support that the USA could plausibly intervene, possibly under cover of an OAS resolution, to come to the aid of a friendly and popular movement to rid the island of a hated dictator. If those had been the facts on the ground, OTL would be very different, Kennedy would have followed through, and Castro would be dead, in hiding or exile.
Those were however not the facts on the ground; Castro had a lot more support than American planners estimated, and the invasion was pathetically doomed barring all-in American invasion in a context where we would most plainly not be liberators. This was a choice point that a different President might have reacted to differently. But the reasons for being reluctant to go all in with option 2 that sent Eisenhower down the covert track in the first place would weigh as heavily on Nixon as on Kennedy--indeed JFK had more to prove than Nixon did. Since Kennedy backed off, but the USA still remained committed to ousting Castro one way or another, it seems a fair chance that Nixon would do the same.
So we have two tracks here. You presume, implicitly, that Nixon would go all in and openly invade. But also that that would simply settle the matter. I would think that Cuba would have to remain under US occupation for a long time, maybe forever. It is true that in Vietnam the opposition had geographic refuges and supply lines while Cuba would be isolated and effectively under as total control as occupation troops could make it. Still I think Castroite support would smolder on underground, and the USA would not dare pull out for fear any government acceptable to Washington would be overthrown the second we left. Cuba then would be something of an embarrassing quagmire, with a certain ongoing death rate for American occupiers and our handpicked Cuban supporters, very likely a repressive police state as objectively bad as Castro's, and clearly worse in some respects (arguably better in others).
Or--Nixon chooses as Kennedy did for the same reasons, and hopes to settle the matter later, as Kennedy so hoped.
I don't think you can dismiss the Missile Crisis in that case, unless Nixon happens not to approve the policy of installing US IRBMs (Jupiters) in Turkey. If Nixon does as Kennedy did, in this respect, then Khrushchev is likely to attempt to balance the scales via missiles in Cuba, which also (primarily, in K's rationalizations) had the effect of defending Castro's Cuba through deterrence. Turkey was in fact given the Jupiter base as a diplomatic move, one likely to be recommended to Nixon and approved by him. Obviously if meanwhile Cuba is undergoing an American occupation then the Cuban missile option is clean out of course--but what would K's fallback be in that case?
It wouldn't be Cuba anyway, nor would it be thermonuclear war save as whatever he does might inadvertently blunder into it--Khrushchev knew the USSR remained terribly vulnerable. You might assume that even if Cuba remained under Castro's control that K would be more deterred with Nixon than Kennedy in the White House, but I think that is dubious. He was driven by personal emotion and would likely rationalize away any perception of Nixon as having better resolve--especially since for Cuba as a friendly Soviet missile base to be an option, Nixon would have to have objectively backed off the same as Kennedy did OTL!
So you don't think he would back off--this means a major military operation by the US forces just months into his administration and after that, lots of those forces would be tied down there in Cuba. And they'd suffer some attrition, and a bit of subversion too I think. He might be able to spin Cuba as a glorious victory and the ongoing service of American draftees in uniform there as a positive. But I think I can guarantee you, it won't be a fully settled matter. And this will have a bearing on the nature of his Democratic opposition in '64.
Meanwhile Vietnam. OTL Vietnam was obviously not yet a major albatross around LBJ's neck in that early year. It seems contradictory to your assumption that Nixon will go all in against Castro, but somehow get out of the Vietnam finger trap. Kennedy did not jump into Vietnam on a whim; he was drawn in incrementally by prior American commitments there--undertaken by Eisenhower and I am unaware of any evidence Nixon would have dissented from Ike's 'Nam policy in the least.
JFK certainly wanted there to be a perception of a drastic change in policy his election would introduce, so there is that grounds to suppose something would be different. He believed it was important to beef up US conventional capabilities to win in small brushfire conflicts so we would not be a paralyzed Gulliver of a superpower. Ike found Democrats in Congress and campaigning for the Presidency to be more bellicose and liable to vote for higher military spending than he was comfortable with, hence his warnings of the dangers of the "military-industrial complex" he named in an outgoing speech. But Richard Nixon was practically the poster boy for the MIC! I am sure that Nixon would differ from Kennedy, but not very radically. For Kennedy, escalation in Vietnam was an opportunity to put Maxwell Taylor's theories into effect.
But the crises that developed in Vietnam posed the same sorts of issues that Cuba did. Again our choices could be characterized as essentially the same three as I listed for Cuba--1) get out, cut our losses before we got really burned, and accept the political consequences of "losing" yet more territory to Communism--this being off the table for either party's executives to even consider seriously--and in the case of Vietnam must have seemed ludicrously premature to say the least. 2) go all in to get a final resolution favorable to us. The risk that doing that in Southeast Asia would indeed escalate into an unwanted global war was much higher there than in neighboring and isolated Cuba. Or, seductive and fatal 3--seek a form of victory taking the form of aiding a scrappy little fledgling democracy (never mind the police state--we say it is a democracy, are you going to question the integrity of the US Goverment?) against Communist tyranny by helping them survive a vicious and insidious secret war waged by a ruthless foe. In this context, every step we took to shore up the Saigon revolving door of serviceable regimes committed us to take another and another. Cutting and running would simply not come up as an option, whereas defining a fixed level of aid, that would keep the outpost of American adventurism under the radar of US domestic politics, and sticking to it regardless of circumstances would predictably lead to a Viet Cong victory as the Saigon regimes we had practically put together by hand ourselves (using largely the cast-off remnants of the ill fated sectors of Vietnamese society who worked for the French before us) was effectively made of sugar, crumbling before our eyes in the rains and attacked by legions of ants. At a fixed level of aid it would not be a question of if but when we'd be driven ignominiously out of former Indochina completely, and domino theory said Laos, Cambodia, then Thailand, Singapore and Malaysia would surely follow, perhaps Indonesia as well and who knows, maybe the Philippines. Holding the line in Saigon would seem essential, and the only way to handle the waves of crises in a timely fashion would be to double down and keep doubling down.
OTL it was not a major issue in 1964 except insofar as Barry Goldwater could be attacked for proclaiming a desire to pursue Option 2, which painted him as a warmonger and the likely trigger of WWIII. Nixon's Vietnam policy might differ in a number of ways, stylistically especially, but he was in the same trap Kennedy was OTL. He could not find an easy way, and the domestic troubles the war would spark in America after Johnson took office in his own right in 1965 were in my judgement not responsive to these details, but to the broad phenomenon of escalating American involvement there. The USA was fighting under the false pretense that they were facing a catspaw operation run by puppet masters in Hanoi who in turn were puppets of the Kremlin, and that by inflicting punishment on the North we could get the civil war in the South to be called off, at which point South Vietnam would become peaceful and American forces could either be withdrawn or anyway occupy a safe ally. Indeed there was some justice in that view as far as Hanoi went--Moscow is another story; Vietnam like China under Mao was a loose cannon the Kremlin had essentially no control over. Certainly the North aided and promoted, and even guided, the southern insurrection--but they would have been pushing at string were it not the case that the South was hardly a viable society in itself. Eventually--via the massive American intervention that so undermined American society--Southern rebels were indeed depleted and the war could continue only with northern cadres dominating the guerrilla movement. But had the South been left largely on its own with only American hardware and a handful of true voluntary advisors to help, they could not prevail, and the effort of bombing the North was pretty much wasted from the point of view of getting control in the South. Without American GI draftees to undertake the various schemes generals like Taylor and Westmoreland tried to break the power of the Communist enemy, the latter would simply overwhelm the weak force the Southern governments could muster from their own people.
Faced with the choice, escalate or go home, surely Nixon would choose the former, and with little perceived reason to hesitate. His cabinet would share Kennedy's sense of ultimate American invincibility and see little reason not to double down, hoping each increment would lead shortly to victory.
Vietnam then would be no issue until after '64 but that is just as OTL was for Johnson. If reelected, his different ideas than the Johnson administration might lead to less frustrating outcomes for the American public, especially if spun right.
However, the US Army suffered quite a debacle in that war, and the fundamental reasons it did again went back long before the election of 1960. Between the growth of careerism in the Army and the total lack of preparation for the type of war the USA had to wage to support the Saigon regime, and the demoralizing lack of any clear sense of what the US was trying to accomplish there that would make any sense in terms of normal US patriotic narratives, the wearing terror of the war, a war with no fronts and no clear victory in sight, really bad things happened to this machine that had done so well in WWII. The rot in morale spread all through the service as soldiers were rotated into the theatre and then out of it again. There is no reason to think the Nixon administration would see it coming or have any plans to forestall it, even by accident, and in Nixon's second term it would bite him on the butt.
Now would the interaction of Cuba and Vietnam change the picture? I think it would only make things worse. Cuba all by itself might be sort of all right--wrong from a point of view like mine, surely we'd be backing a pretty brutal right wing police state while entrenching traditional Cuban poverty, and facing a bitter guerrilla/underground foe who will not perhaps amount to a very large scale but will never lack for recruits either. But even if Cuba turns out to be rather expensive, it won't deter Nixon from being led down the primrose path in Vietnam. Then when the rot of Vietnam spreads back to soldiers in occupation of Cuba, I would think that subversion by Castroites would be more effective than any subversion by Viet Minh ever was of Americans. Not a gigantic thing but it would add a whole new element to the blowback from Vietnam--in addition to all the OTL war protest phenomena, there will be some real Communist subversion of American soldiers and some of them will lead yet more revolutionary factions in the USA, and these might be more pragmatic and have better grassroots traction than the OTL New Left/Yippie types--and indeed might recruit the best and most effective from those movements. By 1968 the situation could be a lot more apocaplyptic than it actually was OTL, especially if Civil Rights are more stalled and there is no Great Society initiative.
All that if Nixon gets reelected. Your interest in who his opponents would be. The choices I am seeing suggest little to inspire!