Following his presidency, JFK was probably going to do what he wanted to do in the first place: writing. I'd imagine the Seventies would likely see JFK publish memoirs of his Presidency, how he handled the Cuban Missile Crisis, the Civil Rights Act, and the escalation of Vietnam. It's highly possible that he might buy the Boston Globe and try to turn it into a world class paper (like the New York Times). That would be a useful tool in maintaining his image following his Presidency and for if his brothers tried to make the plunge in subsequent years (I can imagine Bobby going for it in '76 or '80).
I don't see JFK and Jackie divorcing. Following the death of their son, Patrick, the two had grown much closer and JFK and Jackie, whilst they did have their ups and downs, did genuinely love one another. I'd imagine they might also have another child or two. Jackie was only 34 when JFK got shot, so it's not totally out of the question.
As for where the Kennedys would live, I'd imagine a penthouse somewhere in uptown Manhattan for most of the year, whilst still summering at the Kennedy Compound in Hyannis Port. There was also some talk of JFK renting an apartment at Chatsworth House in England or at the very least spending more time there after his Presidency, which would make sense due to his Anglophilia, his spending time there in his youth, and to it being where his sister was buried.