You have to remember that the number of nuclear warheads of all sorts DOES NOT equal the number of targets that could be hit. Many of the warheads are nuclear armed torpedoes, nuclear mines (land and sea), warheads for air defense missiles (both SAM and air to air), "backpack" nukes etc. On top of that many nukes are warheads for IRBMs or other "theater" nuclear weapons, and also there are more gravity bomb nukes than can be carried on nuclear capable aircraft all at once. Now you get in to the fact that some targets will get more than one warhead/weapon, and that there will be some second strikes against targets where the first strike did not do the job for one reason or another (missile or warhead failure, aircraft shot down, a "miss", etc).
Don't forget that some of the delivery systems such as aircraft will be destroyed early on, so even if there is a bomb for them to drop they aren't there to do it. Likewise subs may be sunk before they can fire any or all of their missiles. Likewise missiles kept in reserve may be destroyed, and also bases where nukes are kept are going to be targets so "reserve" nukes will be destroyed in some numbers.
The key thing the US & USSR are going to try and do is destroy military targets that can hurt them, as well as certain key industrial and political targets. For sure China will get hit, and by both sides. Some neutrals who could represnt a close threat, such as Sweden and Switzerland will be hit by the USSR, and of course Cuba by the US. Priority for hitting Australia and New Zealand even with ANZUS is low, as neither country can do much to damage Soviet interests during the war or even in a post war scenario - perhaps hitting a few bases that can support or would support US nuclear capable forces but very limited.
Hitting South America or Africa is a waste. No threat there and post war the USSR hopes to survive with enough left over "toys" to be top dog. South Africa might get one on Pretoria, or its nuclear establishment but not more.
Any ICBMs fired first or second strike are going to be used against US or NATO, with maybe a few to use against ANZUS or S. Africa but I doubt it. SLBMs would be used primarily against US to hit key targets with minimal warning, or SSBNs hiding away for very delayed strike or post war force reconstitution. IF the USSR wants to hit S. America, Australia, NZ bombers would do the job, however the issue there is range/refueling.
IMHO there would be lots of places "untouched" by a nuclear war in the 1980s. However for many of them, even if not too badly affected by fallout and "nuclear winter" it would be a disaster. Absent food imports from US/Canada/Australia many countries would have severe famines, of course this would mean higher disease rates and many of the "Unaffected" countries do not/cannot manufacture much in the way of medicines and there will be no imported vaccines or antibiotics for some time. You would expect many countries to dissolve in to anarchy with fighting to garner limited supplies of necessaries, warlordism, etc.
A nuclear exchange in the 1980s would be a disaster for most of the world, however there would be large areas outside of Europe/North America/China that would not see much if any direct impacts of nuclear weapons. Both sides had plans (however unrealistic) for a post war existence with remaining nuclear forces. If after the major war the "winner" needed to nuke somebody to make a point who could stop them? For example, a relatively untouched but subservient Brazil is much more valuable in rebuilding the USSR than one that has been hit with descent in to chaos.