Most of the countries in the Northern Hemisphere would be destroyed. South America and Africa below the Sahara would be fine. China, India, and Russia would be destroyed.
I can imagine a situation where there are a series of military dictatorships in South America and eventually one becomes dominant, conquers South America, then Latin America, and eventually encroaches on north america.
I also can imagine a reaction where an African and Pacific union is formed survivors who were not the targets of the bombs. A kind of mutual group that was not hit as badly as the Russians who reunite large parts of the world outside of the wasteland. The African and Pacific union might have to defend themselves from remnants of the United States, China, India, and Russia's military because they might have some radiation free land.
The southern hemisphere does not have many nukes historically. Brazil turned away from producing nuclear weapons. The South African plan for a nuclear weapon never happened. Australia never developed a bomb. Indonesia did not as well. Japan might be an invasion target from Russia because they would have radiation free land.
Israel was supposed to have a secret bomb. It would probably get wiped out along with several surrounding countries. Parts of the middle east would be irradiated.
Most of Asia did not develop nuclear weapons and would be free of nuclear weapons and targets. The bomb might unite different regions of the globe to deal with nuclear winter as well as some of the raiders and survivors of nuclear war.
Canada and Iceland did not have a bomb. Most of Canada would not have been hit by nuclear weapons. I would imagine after the war, they might have problems with surviving states from the United States attempting to annex safe land from Canada.
Europe, Russia, the United States, China, Pakistan, India would be irradiated messes.