I've brought this up on numerous occasions on other 'JFK lives' threads, so I'll bring it up again; JFK's
ailments and issues were going to have killed him by the mid-70's. He was not simply confined to a wheelchair, his issues were a constant plague upon him right until the final moment of conscious, and actively impaired his abilities as commander-in-chief. Doctor's have stated that Kennedy living as long as he did was a miracle; However, let's talk about what life he would live.
He runs in 1964, that's a given. He had made it his clear intention to run and everyone knew it, be it the Democrats, the Republicans, even the milkman. And he would, undoubtedly, win. Now that next four years will be important in securing his legacy. Compared to Johnson, he won't accomplish as much. He may be able to get the Civil Rights Act through and push 'New Frontier' initiatives, but they'll not be as strong as they were IOTL. Additionally, news of his health issues, and the cover-up of them, will come out far before he begins to write a letter for his successor, as the stress of Vietnam, the Soviets, Civil Disruption and a fracturing Democratic Party will do him no good. People will, understandably, feel betrayed by the revelation as he has effectively lied to the people (Not as bad as Nixon, but it won't be great).
Then you have the fun world of Sex Scandals. Kennedy was, to put it simply, a sex addict. The man was addicted to boning. His wife knew it, the press knew it, the milkman knew it, but a public revelation of his Sex Addiction as him actively cheating on his wife will be disastrous for him. Think Clinton but more severe. Atop this, we must also consider how Kennedy would respond to various events happening in office, and how these would contrast to Johnson. Vietnam will likely still escalate, even if a withdrawal plan was in effect, and riots will still happen, his handling of them probably similar to Johnson's.
Now, Kennedy leaving office will be a frail, sickly man, plagued by failing health and national controversy. His public life will be curtailed by physicality, so him going on a massive nation crossing tour to talk about how cool stuff is will be out the question. However, a more likely outcome will be him returning to writing, particularly about Modern Events and his Presidency. I imagine he'll fling shit as Nixon, who'd almost certainly run in '68. If he lives long enough to see 1976/80, he'll support Ted or Robert if either goes for the election, although this support will not be all that much. On other matters, I can see him be fairly liberal, or at least open minded, about much of what's happening.