The Vasily Arkhipov scenario, with a twist.
Many answers have hinted at just how important it would be to determine exactly how the specific scenario plays out, but I haven't seen any take this concept and run with it.
During the Cuban missile crisis, Vasily Arkhipov is often credited with preventing a Soviet nuclear strike and, potentially, an "all out nuclear world war 3" that very likely would have ensued afterward.
So for your world building setup, you'll need to start with a similar situation: competing/conflicting world powers gradually increase tensions until someone goes too far with their posturing and threatening behavior, and the other side feels they have no other option but to launch a pre-emptive strike, but this time there's no Arkhipov on site to stop it.
Which nuclear power is most likely to launch such a strike? Most answers speculate that it would be North Korea, while others mention China, Russia, Pakistan, and the US. NK is, hands down, the most frequently mentioned, for obvious reasons that I don't feel the need to include in my answer. But personally, my money says it's actually the US that launches the first nuclear weapon...at NK...in response to what they believe to be a clear and present danger to themselves from whatever antics NK is up to at the time.
From this point, just work through the responses of all the other nuclear powers. I suspect US would launch a single strike, hoping it will be enough of a deterrent, on its own, to prevent further conflict. But they will also certainly have their finger 'on the button' of many more, just in case. NK will not have any Arkhipov stand-in available and will certainly retaliate, and China will join in, though not "all out" at this point. China will hope to "nerf" the US nuclear capabilities and end the conflict that way, but NK is not likely to hold back anything that the US didn't destroy with its first nuke, they'll launch it all. As soon as the NK nukes are detected, the US will respond with enough to make sure NK has no threat whatsoever left, but will only attempt to "nerf" China in the same manner that China attempted to "nerf" the US. While the US volley is still in the air, the "all out nuclear war" phase kicks off in earnest as China and anyone else that thinks China might win, will send their "all out" volleys at US targets, prompting the US and their allies to send their "all out" volleys in return. But hopefully by this point, some of the initial "nerf" attempts have at least partially succeeded, dramatically lowering everyone's nuclear arsenals, with relatively low impact on civilian populations during that phase. The "all out" phase would see many population centers targeted that the "nerf" phase was unconcerned about, but with reduced firepower the choice of targets would have to be more selective. NK would launch all of theirs before getting hit by the first US nuke. US and China would both be heavily nerfed. Their allies would likely launch most of their nukes before being nerfed themselves.
In the end, only Russia and the US, and possibly China, have enough nukes to strike a relatively large number of targets even after the initial "nerf". US will strike NK and China, and anyone that joins them. China will strike the US and anyone that joins them. I must say I'm not sure what Russia might do, they could pick either side, for a variety of reasons, or they could try to wait till US and China beat themselves up, and then finish them both off (India and Pakistan might also try this type of thing, waiting till the big three pummel each other, and then try to kick them all while they're down).
But the point is that, with the sole possible exception of NK, none of them will be trying to destroy the world, they'll all be trying to make the whole event as tactically precise as possible, and end things as quickly and cleanly as possible, if for no other reason than self preservation, as an uninhabitable world doesn't benefit them in the slightest, and they know that. So primary targets will be nuclear launch capable facilities for the vast majority of the entire conflict, until no one knows of anyone else's nukes that haven't already been launched or destroyed. At that point, the conflict will turn to attacks on other military installations and population centers in retaliation for any missiles that still come in from launch sites that weren't known far enough in advance to be targeted in the "nerf" volleys. But most parties will quickly cease fire when they realize that any missile they launch, and even other, non-nuclear military actions, will be met with nuclear retaliation against their biggest, still-standing, population centers.
When the dust settles, the devastation will indeed be massive, and widespread. The fallout will certainly be a major issue. But because of the tactical precision from most of the missiles involved, and the targets selected, there will be large areas of the planet that are, relatively, unaffected. Nowhere will be entirely untouched, certainly, but there will be plenty of reasonably intact land to go around.
Personally, I'd pick rural inland Brazil, but the area surrounding Lake Victoria in Africa would also be good for similar reason to my selection of Brazil:
These are climates good for agriculture, and which are likely to remain good climates for agriculture, even with mild cooling of the climate from nuclear-winter-like effects. (At this point I'm operating under the assumption that, for whatever reason, nuclear winter will not be so severe that your story fails to have a starting point at all). The choice of what to plant might have to change with the climate, but that's true of anywhere in the world.
Political stability before the nukes is not likely to be relevant, as chaos will ensue, worldwide, and it's very unlikely that any currently existing country will remain intact in the aftermath. The world will be reduced to city-states and barter systems, if not worse, so whoever is in a particular region is not likely to be able to migrate far, at least initially, and is not likely to care what another group of people even a meager 100 miles away is doing. They'll be interested in sustaining themselves, and cooperation for survival with anyone else in their local area is as good a reason to form a clan/tribe/etc. and get to the business of making food for their new community. No matter where you end up, it's going to come down to luck of the draw whether you end up in a group that decides to farm, a group that decides to hunt, a group that decides to loot, etc. So the original government of the area isn't really a factor to consider. Instead, potential food productivity of the land is likely to be the deciding factor for if and when a region regains some semblance of civilized society, so getting to such an area in advance is your best bet for finding the higher number of farmers to cooperate with and the lower number of looters to contend with.
They are not likely to be significant targets in any phase of conflict, and are not likely to be downwind for fallout of any significant targets during any phase of the conflict. Sure, they might have alliances, allegiances, treaties, and agreements, with parties on either side, but they don't have any strategic or tactical importance in the actual nuclear aspect of the conflict. Again, nowhere on the planet will be entirely immune, but these two places should receive the lowest portions of both direct and collateral damage.
I just picked Brazil, over Africa, because I'm more familiar with it, and I suspect its agricultural potential to be even greater than that of Africa (though I admit that could be a misconception based on my own bias).
