Propably the USA would avoied the war in Vietnam. Johnson wasn´t so interested in foreign politics like Kennedy.
I disagree. JFK continued to send advisers and prop up the South with arms and supplies, which I doubt Johnson would have withdrawn. Johnson, if I recall, tried to get Kennedy to take a harsher stance with more active troop support.
There's a few things Kennedy did which I'm not sure Johnson could have, mostly because you have Kennedy utilizing support in the North and Johnson in the South. Without Kennedy, Johnson may not have had enough Yankee support. Then again, it was Johnson's own arm twisting which managed to get a lot of the New Frontier legislation passed so he could easily do it on his own.
Do the Civil Rights acts of 1964 and 1968 get passed with Johnson alone? I'd think so. Kennedy had already instilled a call for greater Civil Rights under his administration in the future (which he carried out), so Johnson probably would follow through that call. Though how it would look in the end is debatable and the Conservatives in Congress who tried to stop it could have had less support if Johnson waves around the memory of a dead leader.
Does the Cold War cool as it did? Maybe, but if Johnson goes warhawk in Vietnam as Kennedy didn't and remains closed to the dialogue Kennedy opened up with the Soviets by '65, I think you could see the hostilities continue to rise rather than begin to set. By the time you got to 1964, Kennedy had been becoming less and less hawkish (though not a hawk to begin with), though still a Cold Warrior, thus allowing for a firmly negotiated yet peaceful relationship.
As a result, do we ever see the joint American-Soviet moonshot in '72? If the Cold war remains as tense as it may have been, probably not. Though you may still see the US reach the moon sometime in the late 60's or perhaps pushed off to the early 70's (or perhaps even later). Frankly, I don't know Johnson's view on NASA too much.
But most importantly, does the New Frontier continue under Johnson? Perhaps, since he supported medicaid and food stamps and all those things with JFK and since he was a Roosevelt-Democrat. Then again, its hard to tell how much an assassination would shake things up in America.
OOC: JFK was planning on opening a more peaceful relationship with the Soviets and did, in the OTL, think of a joint moonshot and I think he proposed that to Kruschev at least twice. And Kennedy was moving toward propping up South Vietnam while trying to avoid active troop involvement if I recall. And JFK had become very active in supporting Civil rights by the time he was shot (the debate that he wasn't I think comes from the "Static man" theory of history which I think is wholly a bad model).
So I'd say its like the OTL, minus Vietnam and hippies, with better relations with the Soviets, but still with sideburns.
OOC: Out of pure morbid curiosity, why do you repost the same thread two weeks after you already posted your own answer?
OOC: Perhaps to remove the whole Global Thermonuclear war bit.