My take: The 1950s proceed much like in OTL, maybe Joseph McCarthy is assassinated by a communist agitator around 1954 which makes McCarthyism seem justified and there are no Army hearings so McCarthy's reputation is saved. Stalin still dies off in 1953, Ike becomes President, the Korean War could have gone in a full American victory and no North Korea but tensions with China rise due to encroaching U.S. presence on its border. In 1960 Nixon becomes President, initiates Civil Rights but the Hippie culture is looked down as possible communist sympathizers and crushed. The Vietnam War could have escalated into the U.S. declaring war on North Vietnam (In Fallout:Tactics which is semi-canon, a radio broadcast is heard of the U.S. declaring war on Vietnam). The outcome of the war could've resulted in a second-Korea style with China once again interfering militarily by sending troops down and eventually sparking a permanent stalemate by the late 1960s say 1968. China's intervention in the Vietnam War further sparks tensions between America and China.
The Sino-Soviet Split still occurs around 1961, China makes an Atomic Bomb around the same time in 1964. China still has occasional border disputes and battles with the Soviets throughout the 1960s-1970s. Nixon might make the opposite decision to visit the Soviet Union instead of China to meet Premier Khrushchev and the Soviet Union begins to liberalize to lessen nuclear tensions with America especially with the threat of a resurgent China which is beginning to become the third superpower. After Mao's death in 1976, the Gang of Four successfully take power and purge many officials who would liberalize China in OTL like Deng Xiaoping.
Cuba's Revolution is a failure, the Bay of Pigs invasion is a success and Cuba is brought back under American influence so no Cuban Missile Crisis. No Cuban Missile Crisis could mean Khrushchev isn't ousted in a coup in 1964 and thus his reforms continue. The Hardliners in the Soviet Union are slowly removed over the course of the 20th Century.
The 1970s see tension in the Middle East with wars like the Six-Day War and the Yom Kippur War occurring. Detente with the Soviet Union never ends, the Soviets never get into the quagmire that is Afghanistan. Iran might stay American aligned if the Iranian Revolution is put down and the Shah is restored. The Arab World remains under the control of Secular Dictators and the rise of Radical Islam is crushed and never becomes a major issue until the mid-21st Century.
The 1980s are the Reagan Era (as hinted in Fallout 2 which mentions the economy at its best since the Reagan Era). A tougher stance on China is made while Gorbachev-esque leaders in the USSR pursue closer ties to America. No Chernobyl in 1986 so Nuclear Power's reputation is saved and continues to be a popular form of energy.
The 1990s see the Soviet Union enter an economic recession which sees it slowly lose its superpower influence and China to fill in the gaps with funding communist groups throughout Africa (which went through decolonization like in OTL). The U.S. might provide some financial aid to keep the USSR from collapsing since its a good buffer state against China.
The 2000s see a technological renaissance with new robots and other atom-punk technology appearing in the markets around the West. First prototype robot servants are invented. The European Commonwealth comes into being.
Finally by the year 2017 in the Fallout-Verse, the United States is enjoying a period of economic growth with the beginnings of colonization of the moon (as seen from the Museum of History in Fallout 4 which mentions moon-bases), China is looking to catch up and has its own space program. The Soviet Union is beginning to stagnate and while still considered a military superpower, many foreign affairs experts see the USSR as a shadow of its former self as it's unable to exert itself on the globe as much due to financial strains. Ethnic tensions run high in the nation and the Warsaw Pact is looking to collapse any second now with plans by the Soviets themselves to let go of most of the Eastern Bloc except East Germany, Czechoslovakia, and Romania.
That sums up my interpretation of how things went, I know there's a lot of holes in this but this is a rough sketch. What do you think?