I think 1968 would be the ideal year to re-visit BECAUSE the times were so tumultuous.
Of course, time travel would be conditional upon the traveller having a "watch and observe" brief only. Don't go changing anything, now. No popping into the hotel kitchen and telling a cop "That guy over there's got a gun and he's gonna shoot that nice Mr Kennedy".
Some years ago I spoke with somebody who claimed to have been at the US Embassy demonstration against the Vietnam War in London that year. It started (he claimed) as a peaceful demonstration, but it was suspected that agents provocateur must have been placed in the crowd. It seemed that the police were just a little too well organised.... too well positioned in a tactical sense. They responded just a little too quickly when the trouble kicked off. As if they were... I dunno... "expecting something to happen", perhaps..?
That's his version of events, anyway.
Your summary of the year left out a couple of the key events. The Tet Offensive in Vietnam wasn't successful in that it won the war, but it was the beginning of the end for the US military in that country. The Pentagon Papers later revealed that Johnson, McNamara, et al, had always known the war couldn't be won, but Tet made it glaringly obvious to the whole world.... except for Richard Nixon, who had won the election on a "Bring The Troops Home" ticket but still stood by the Diem Regime. True, he did withdraw American forces but his policy of "Vietnamisation" of the war cost hundreds of billions of American taxpayers dollars in equipping the ARVN and also led to the bombing of Cambodia. Oh, what a mess it all was.
You mentioned the circumnavigation of the moon that Christmas by Apollo 8, which, after the launch pad fire in Apollo 1 the year before had nearly caused the cancellation of the whole programme, achieved so many mission objectives in one big Hail Mary pass that Kennedy's target date of the end of the decade became possible again.
The "Earthrise" images taken by Jim Lovell were astounding but what must have sent an almost primal shiver down everybody's spine was the recital, on Christmas Eve, of The Creation from the book of Genesis. Magnificent, not just in a theatrical sense, but so deeply meaningful to everybody here.... on the Good Earth.
The crew of Apollo 8 saved 1968.