United States of America
Politically, the US is fairly moderate. Congress returns to the hands of the Republicans after four years of Democratic control, under President John Kerry. No "Great Society" ever emerged, though complaints about the corrupt "welfare state" resounds with Republicans, as well as some conservative Democrats. Kerry who ran on universal health care for all Americans, succeeded in getting it passed with Bipartisan Support, but now faces lame-duck status with Republicans looking to roll back tax hikes and curtail spending.
Economically, the USA is the strongest nation on Earth, with gross domestic product rates equivalent to OTL's 1980s. Most of the country has recovered from "The War" (as it is often known) and population levels are nearly back to pre-1956 levels.
Among the cities destroyed, only three have been re-built: New Chicago, New Los Angeles, and New Seattle. The "Manhattan Peace Park" was fully re-forested and is maintained as a national park. Adjoining former boroughs, Queens, Brooklyn, Bronx, are independent cities.
Socially, the Civil Rights Movement came nearly a decade later than OTL. The George Wallace Presidency split the Democrats for years, but eventually liberals took it over and made it comparable to the Republicans. After the release of Martin Luther King Jr. in 1974, the movement flourished and Ronald Reagan oversaw the creation of much of the modern civil rights movement as well as school and public facilities integration.
By 2006, America's race relations are equivalent to a less-turbulent version of OTL's 1980s. Affirmative action was never established, but stricter anti-discrimination laws were created. With no school busing, the "white backlash" of OTL's '70s never came, though integration is about the same as OTL.
The "Sexual Revolution" came after the War, with Government approval of abortion for radiation-induced mutations and birth defects. By extension even healthy fetuses could be terminated as it was left to the States to decide how much discretion the doctor had in proscribing an abortion. Contraception became easily available during the Reconstruction Period of the early to mid-1960s and "free love" (less the hippie connotations) emerged in the early 70s.
No "Green" or "environmental" movement has begun, due to no fear of over-population, national re-forestation attempts (primarily in areas destroyed by nuclear attack), and Government oversight of chemical usage (a holdover from Reconstruction).
Technologically, without the space program of the 1960s (satellites were launched again in the mid-60s, a manned orbital flight in 1974, and lunar landing in 1993), technology lagged behind OTL. Cable television first became readily available only in the early 1990s, while the "CompNet" (this ATL's version of the "Internet") is only now becoming popular. ("E-bay" and "amazon.com" come into being in 2010).
Increased fuel efficiency, demanded by the lack of oil imports in the early 60s, revitalizes Detroit in the 1970s, though a type of SUV is starting to gain popularity with relatively cheap gas. Air travel is along par with the 1980s, though trains (vital during Reconstruction) still carry a fair amount of passengers.
Oddly, nuclear power is on the rise in the US, as public fear of "meltdowns" (like OTL) was in fact LESSENED due to actual contact with fall-out and atomic destruction and the recovery of the US from the war. By 2006, 40% of America's energy supply is nuclear fission.
As of 2006, most Americans enjoy a reasonable standard of living, though cancer rates and birth defect rates are double pre-War America. Psychologically, many of those past the age of 40 suffer extreme forms of Post-Traumatic Stress Syndrome and Medicare (created by George Wallace in 1973) covers mental health due to this.
Canada & Mexico
Canada lost Ottawa and Vancouver to Soviet nuclear attack. The capital was re-established in Montreal. Recovery paralleled the United States and strong economic and political ties helped Canada return to its pre-War state by the late 70s.
Mexico went through several fascist "Peron"-style leaders, but eventually became a moderate European-style social democracy. Lots of Reconstruction work in the US drew a lot of immigrants, but the growth of the Mexican oil industry and rising middle class made illegal immigration as in OTL almost unknown.
Central & South America
The rise and fall of the "Somoza/Peron/Pinochet" dictators continued much as in OTL. By the 1990s, many reformists had taken power in Brazil, Argentina, and Chile, but without Soviet sponsorship, Marxist guerrillas failed in Cuba, Nicaragua, etc.
The economic prosperity of Mexico pushed many towards that model and by the 1990s, most of Latin America was similar in nature to the "Costa Rican" model in OTL.
Castro and the "26th of July Movement" members found themselves stuck in Mexico for much of 1956 (instead of returning to Cuba in November 1956 to attempt to overthrow Batista). Finally, in late August 1957, they attempted to take the "Granma" yacht back to Cuba, but were intercepted by a US Navy ship patrolling for still-active Soviet submarines. Awkwardly identifying themselves as "turistas", the captain of the "USS Noa" (DD-841)ordered their arrest and took them back to Guantanemo Bay. Batista's forces arrested them and later executed Castro, Che Guevara and many others.
The United Kingdom has recovered to pre-War levels by 2006. London was rebuilt, with replicas of Parliament, Hyde Park, and Buckingham Palace upon the previous sites. It remains a strong ally of the US, but decimated France and Germany are now in their third decade of attempted recovery and embarrassment at being the "welfare recipients of the world" have caused them to be bitter towards America.
The former Warsaw Pact nations are faring no better. From Poland to Hungary to the now disintegrated Yugoslavia, each is facing starvation-level food production and distribution and basically living on the foreign aid from the United States, Canada, and Scandinavia. Former Soviet republics, like Ukraine, are in similar shape.
A great deal of Europe is uninhabited. Vast stretches across the battlefields of The War have gone fallow and some forests (gone since the Middle Ages) have re-grown.
China, capitaled now in Chongqing, is still recovering, but has begun a re-industrialization program with some capitalist incentives. American corporations are allowed to develop and own factories in China, though unlike OTL, the lack of trained workers means that goods are not cheap enough to export to the US and remain in Asia.
The Soviet Union
The Soviet Union as such still exists, though its actual area of control is smaller than OTL's Russian Federation. Premier-General Vladimir Sergeyevich Mikhaylov is the leader of the New Presidium in Achinsk, still "temporary capitol". Relations with the US are strained but amicable, given aid packages approved by President Jimmy Carter in the mid-1980s.
Like outlying areas of China, much of the former Soviet Union is not even under the control of the Soviet government. Local warlords, some swearing loyalty to the Achinsk government, but some not, rule in Siberia and Kazakhstan.
The average Russian is so incredibly impoverished that they resemble OTL's Ethiopians.
The Middle East
This timeline's Middle East resembles OTL's sub-Saharan Africa. Most of the major countries from Morocco to Afghanistan are run by sheikdoms, theocrats, and secular dictators. Though Islamic fundamentalism never rose as powerfully as it did in OTL, due to decreased Western interference, petty squabbling and jockeying for power kept any sort of "Arab League" or even "OPEC" from forming.
Playing one oil producer against the other, the United States and Europe have kept the price of oil down, though production is still at pre-War levels, except in Iran. With no Soviet Union to turn to, most dictators in the Middle East are capitalistic and have good relations with the West.
Israel remains a superpower with their taking of Egypt and the West Bank. The Arabs refuse to launch an attack against Israel, for fear of getting captured. In 2007, Israel signed a peace treaty with all her Arab neighbours.
Africa remains much as it is in OTL. Sub-Saharan Africa is dominated by dictatorships, though colonialism died out entirely by 1989 and the fall of Rhodesia. South Africa fell into civil war in the 1960s, resulting in the apartheid regime being confined to the Cape Town metropolitan area. The rest of South Africa became the Confederation of the Southern Bantu Peoples, which each native African ethnicity getting their own autonomous state. Whites were given a choice of either integrating into the new nation or joining the racist government in Cape Town. Many urban Afrikaners moved to Cape Town, while rural Afrikaners and Anglo-Africans stayed in the CSBP.
The United Nations
Destroyed in the attack on New York, plans for a "New United Nations" have been stalled for nearly 50 years. With the Soviet Union in chaos, no impetus for China or the Middle Eastern or African nations to join, and seeming failure of the previous institution to prevent The War, the movement has little support outside of American liberals and some in the UK.
Note: Senator John F. Kennedy happened to be at the United Nations on November 11, 1956, and was killed when the Soviet atomic bomb destroyed Manhattan.