Nixon the Dull
Most likely no Bay of Pigs debacle as a) he decides not to let it happen, or b) provides sufficient support that the landing succeeds. However, the Batista regime is still remembered in Cuba, so the counter-revolution may exist only by continued US "assistance". With Cuba being easily blockadeable, the war there ends rather quickly.
In either event, Nixon does not want to get bogged down in Vietnam, and without the military incompetents Kennedy suffered (like McNamara's Band) neither does the US destabilize the Diem regime.
Without a Vietnam War, the Hippies remain a small fringe like the Beatniks of the previous decade. The counter-cultural revolution does not happen. (And a lot of good music evaporates.)
It is too early for Nixon To Go To China, so someone else does that.
1964, the Conservative Movement does not get a boost from the Goldwater Campaign, as Barry supports Nixon.
Nixon would have a narrow shave in 1964 in getting reelected. No Plumbers, as he wouldn't be as paranoid as in OTL. JFK 's health would probably prevent his running, and LBJ wouldn't want to leave his beloved Senate, so the Democrat most likely (I say with a pinch of irony) would be Humphrey. Assuming a fair amount of prosperity, HHH would lose.
Nixon could leave the White House in 1968, still fairly young (as Presidents go) and having an administration noted for it's lack of drama. His remaining years recognized as the Premier Senior Statesman of the Republican Party and Chief Kingmaker.