I don't think this is as hard to achieve as most think, but it does require some changes, particularly with the UN.
The UN is formed in 1946 as IOTL, but pressure from America and Britain leads to it being a group of democracies only, and that full UN membership requires the countries involved to be nations with a certain set of requirements - democratic elections, freedom of speech and assembly, et cetera. Most of the Western world post-WWII has these, but the Soviet Union does not and Stalin objects to the idea, which leads the UN to be founded without the USSR and its allies. By the early 1950s, the countries of the UN are almost entirely allies of the United States, United Kingdom or both. Japan and West Germany join in 1953 and 1955, respectively. South Africa is kicked out for its racist apartheid policies in 1961, but returns after apartheid crumbles into history in the late 1970s, gaining its membership back in 1980.
The United Kingdom works with the United States and the "white dominions" to help adjust its colonies into democracy. India is not partitioned, and joins the UN as a unitary state in 1947, followed by its colonies through the 1950s and 1960s. France does the same, though France's efforts to have its colonies transfer into democracy is not successful in a number of cases.
The exploits of black servicemen in America in WWII lead to a sense among many veterans that racism is counterproductive and doing more harm than good, and most cities with large black communities see large number of black police officers join their forces in the 1940s and 1950s. After the Brown v. Board of Education decision in 1954, black students start arriving in "white" American schools in numbers. In places like Detroit, New York, Miami, Chicago, Los Angeles and much of the Rust Belt, this goes fairly smoothly, owing in large part to the fact that many American blacks gained the respect of their peers in WWII. The development of the automobile leads to the building of the Interstate Highway System, which begins in 1956, though then-President Eisenhower endeavors to have America have the finest transportation system in the world in every regard, and the funding of the time also goes towards railways, air travel and everything else.
A February 1957 investigative journalism article in Life Magazine exposes plans by General Motors and other companies to buy up streetcar systems and dismantle them in favor of buses - which earns GM and its partners in the scheme a congressional investigation and over a billion dollars in fines, and leads to public outcries to save many of the systems that GM was seeking to buy and dismantle. This bad publicity and money problems end GM's attempts to destroy streetcar and light rail transit systems - in fact, GM does the exact opposite, and by the middle of the 1960s is providing funding for expansions of mass transit systems, hoping to sell additional rail cars and equipment.
Over the 1960s, the exodus of middle class families from inner-city regions is met with newcomers coming to clean up their neighborhoods, which means the massive decay of American inner cities that happened in the 1950 through the 1970s largely stops about 1965. The blueprint for the future grew out of the infamous Cabrini-Green housing project in Chicago in the middle of the 1960s, as newcomers of all races began staking claims in the neighborhoods, fixing up buildings and vocally fighting the gangs and racial tensions, which leads to numerous incidents of violence in 1965 and 1966, but the newcomers refuse to be intimidated, and the gangs are eventually driven out and broken up. This tenant activism was soon added to by tenants making changes to the area and fixing up the buildings themselves, whether the authorities liked it or not. By the 1970s, similar stories were happening across the United States in housing projects and communities. Cabrini-Green itself becomes a symbol of misguided urban planning ideals being transformed by the people who live there - and the activist spirit of fixing up the problems in your own communities swells across the United States. By the early 1980s, Cabrini-Green is the center of a growing young person and immigrant community in Chicago's Near North Side.
Jane Jacobs' stopping of the Spadina Expressway in Toronto in 1971 becomes a major rallying point for communities across the United States, and the activist spirit of the time leads to many such situations. General Motors, which had instigated much of these plans, starts jumping in to try and make them evolve to suit new realities, with GM-sponsored projects proposing everything from burying expressways and building parkland or rail corridors above them to building elevated rail lines and stations for them above the freeway corridors. Local banks and businesses specialize in building improvements for local communities, with a popular comment being "If its good enough for people to live there, its good enough to justify makiing people want to live there."
The first American civilian nuclear power station is inaugurated at Shippingport, Pennsylvania, in 1958, and over the 1960s and 1970s nuclear power plants spring up all over the place. An anti-nuclear movement still gets some plants stopped, namely ones in poor locations. March 28, 1979, is just another day at the Three Mile Island nuclear power station in Pennsylvania, and the Nuclear Regulatory Commission gets a reputation for being harsh on those who violate public trust. Improvements in design and engineering standards mean that nuclear power stations built in the early 1970s and later are considerably better than earlier facilities. By the time Shippingport closes in 1981, 176 nuclear reactors are operating in the United States, with an addition 52 under construction, despite the anti-nuclear lobby and its considerable influence. The ire of the environmentalists had, by then, turned to other areas, though the anti-nuclear movement still protests regularly. The most infamous mistake of the nuclear movement was the Shoreham Nuclear Power Plant on Long Island, which never operated commercially, and after years of tests was closed for good in 1990. Such failures, however, did not stop the industry from continuing to expand its operations. By 2010, 265 nuclear reactors operate in the United States, producing very nearly 50% of the United States' electricity.