This is actually very easy - have the Ohio recount go in favor of Bush in 1976. The 1976 election was a close one, as Kennedy couldn't really hammer Bush on his pardon of Nixon seeing as how he had a lot of other skeletons in his closet and couldn't do so without being seen as a hypocrite.
So, what if Kennedy had lost in 1976, leading to a second term for Bush? Well, for one the electoral college would be intact, as Bush winning the popular vote yet still losing made it a target of the GOP, and it being abolished with the 27th amendment was a defining moment of the Reagan administration. Bush would probably have the same foreign policy as Kennedy, though perhaps a bit more hawkish towards the Shariati government in Iran, but overall no change too major. Bush would have also tried to bring forth the initiative to make America a nuclear nation, leading to a better economy and giving whoever the Democrats nominated in 1980 a much harder time (much as how Kennedy's initiative to make America a country powered on nuclear made the 1980 election a lot closer, though thankfully not as close as 1976).
Perhaps we might even see a more left-leaning America. The dubious circumstances in which Kennedy was elected led to a right-wing backlash against not just him but the ideas he represented, that of New Deal liberalism which ever since the 1960s have been leading to a growing conservative movement, one which had its heyday in the 1980s and early to mid 1990s. While a Democrat elected in 1980 following Bush wouldn't have had as much of an impact on his party as Reagan did if said Democrat could be re-elected after 1984 it could demoralize the conservative movement enough to have it either a. moderate or b. whither away following years of failure.
Overall America was in a crossroads in the 1960s and 1970s and changing an entire election result could lead to an America perhaps unrecognizable today.