Eisenhower did have a serious heart attack in September of 1955. If he hadn't survived that, Richard Nixon would've become President 14 years earlier than IOTL.
NIXON IN 1955
Suez Crisis - probably takes a pro-British stance if not a neutral stance; in private, Nixon had said that betraying the British and French was not the right thing to do.
Hungary - probably a similar stance to Ike, strong denunciations but little else. The US wasn't going to start World War III over Hungary.
1958 Recession - much more aggressive response, probably some sort of 'We Are All Keynesians Now' speech and probably pump priming the economy
Civil Rights - stronger response to Civil Rights than under Ike. Probably a stronger 1957 Civil Rights Act (possibly passed in 1958 and with more political capital put into it, there'd likely be no 1960 Civil Rights Act). Possible he'd go for a Voting Rights Act after the 1960 Election. Probably more of a colourblind approach to Civil Rights rather than Affirmative Action.
Cuba - Nixon in '54 either butterflies the Cuban Revolution entirely or butterflies its success. In the event that it does succeed, the US will intervene in a fairly short amount of time (probably before the 1960 Election to improve Nixon's public image).
1956 Election - Nixon vs. Stevenson: Nixon wins by similar margins to Ike. He'd be less popular than the man who was the engineer of the Normandy landings, but he would have the sympathy vote.
1960 Election - I don't think JFK would run against an incumbent, likely LBJ, HHH, or Stevenson get the nomination. Nixon would likely win due to the stronger economic response, enacting a CRA, and defeating Communism in Cuba.