What if Nixon runs in '64? Supposedly, he thought about it, but decided (rightfully) against it. If he ran (perhaps having won his gubernatorial contest first), and stayed in past the assassination, he'd more than likely lose to Johnson. And even if he wanted to, I doubt the Republicans would let him have a third go-around in '68.
So the '68 election is an open free-for-all for the Republicans, and Goldwater wins it similarly to the '64 situation. With the Democrats in disarray all their own (Vietnam, Bobby Kennedy, McCarthy, anti-Johnsonism), Goldwater has a much better chance of winning.
So:
1960 (OTL): Kennedy / Johnson (D) v. Nixon / Lodge (R)
1964: Johnson / Humphrey (D) v. Nixon / Rockefeller (R)
1968: Humphrey / Muskie (D)? v. Goldwater / Miller? (R)
1972: ??? (D) v. Goldwater / Miller? (R)
1976: ??? (D) v. ??? (R)
1980: ??? (D) v. Paul / ??? (R)