TL;DR: It depends on what you mean by "all out nuclear war", and whether or not you plan to remain in the same place post-war... but generally speaking, the farther north or south of the equator, the better, with both the north and south poles receiving the lowest exposure over time due to more self-contained wind patterns. Politically speaking, it's really anyone's guess what might happen, so I'd say you have creative free rein on that.
As for physically surviving the weapons themselves, consider this: by 1962 (after hundreds of above-ground tests conducted by the US, USSR, UK and France), there was no place on the surface of the Earth where radioactive isotopes from nuclear weapons could not be found, thus prompting the first international treaty to limit testing in 1963, followed by the "SALT" talks in the 1970's.
So if you're talking about the "mutually assured destruction" scenario from the time of the Cold War, where literally thousands of nukes would explode on the same day, then the dispersion of radioactive material would be so immense that no place on Earth would be even close to "safe" for many years, possibly even resulting in the fabled "nuclear winter" scenario (nobody really knows for sure). An "all out nuclear war" today would likely involve far fewer, but they are also likely to be far more powerful weapons, thus producing higher local damage with less global fallout. Either way, if any combination of the major nuclear nations today engaged in an "all out nuclear war", it's pretty safe to say that a very large portion of life on Earth would be extinguished within about 6 weeks time, mostly due to the global dispersion of neutron-active isotopes. Of course, due to the enormous number of people on the planet, there would still always be some survivors living in pockets here and there depending on their local geographies and prevailing winds.
There are two primary radiation risks. The first is the the instantaneous (speed of light) exposure to the immense energy released by each blast. This is full-spectrum electromagnetic energy, from long-wave, to infrared (heat), all the way through the visible, x-ray, and even gamma rays. The exposure to this would generally have the same devastating impact on all life forms above sea level that are not at least partially protected by very significant barriers like mountain ranges. (Some x-rays and all gamma rays would still pass through mountains, but the lower frequencies will not.) The intensity of exposure will depend on distance. 435
Line of sight exposure drops off at the rate of the inverse square law (at double the distance, one receives one fourth the intensity; at triple the distance, one receives one ninth the intensity, etc.). If a human is exposed to this direct radiation and they survive the blast, they may have severe burns, or extreme dermatitis which may still kill some in the first hours or days. Marine life would be minimally impacted by the initial blasts, affecting only that which is close to the explosion.
The other risk is, of course, the fallout. It would affect all surface life that receives it. It would affect marine life as well, with the worst effects in the shallow regions and less so in the deep. There are many factors that affect the amount of radioactive particles that get ejected into the stratosphere, among them the proximity of the detonation to bodies of water and the altitudes at which the individual weapons are detonated. Most of the deadly radioactive isotopes created by a nuclear explosion are very heavy, and would gradually, but slowly, sink into the ocean depths, but losing their effect over time.
Radioactive isotopes decay at roughly a rate of a 7:10 ratio between time and intensity (for each 7x increase in the amount of time since the blast, the radioactivity of its fallout decreases by about 10x), but the bigger the blast, the more of those isotopes are floating around in the first place and eventually it all settles on the ground. Most estimates speculate the lethality of any particular bomb's fallout to last on the order of months, but of course, the areas closest to ground zero will receive the greatest volume of fallout and will remain dangerous for a longer period of time.
Bottom line: there are such a large number of variables affecting survivability that for your world-building task, a tremendous range of outcomes are plausible, which gives you a lot of wiggle-room to create it the way you want. In order to minimize the overall threat, my advice would be to focus on dry mountainous regions located at latitudes greater than 30 degrees either north or south, with locations on whichever side of the mountain range receives less precipitation. At between 30 & 60 degrees of latitude, the drier side of the mountains would typically be the East side, and at even higher latitudes, the drier side of the mountains would typically be the West side.
Best of luck with your project. 435