Australia, New Zealand, and South Africa would probably be treated like de facto members of NATO, though given their distance from Russia and lack of serious power projection, they probably wouldn't be hit very hard. Mexico, the Philippines, and Switzerland might be attacked as well, for the same reason. Other than that:
Nobody outside the nuclear planning staffs of the US and Russia knows, and they're not telling. In fact, at least for the US, even the planning staffs don't know, not for certain. At least in theory, the SIOP hasn't been a single plan since the 1960s, it's a menu of options with various withholds, so the president could, e.g., chose to hit Russia but exclude eastern Europe and China from the strike. How that would actually work in practice, and whether or not a president would choose that in the pinch, we've fortunately never found out. I don't know if the Russians have a similar approach, or if they still have a rigid plan.
That said, I'm generally pretty skeptical of claims that either side planned to target third parties in a major way during a nuclear exchange. I've never seen any evidence that this was planned. There are a few exceptions: US and Russian naval and air bases in third party countries, for example, like Subic Bay in the Philippines, those would probably be hit. Possibly major oil infrastructure. But, in general, the claims that one or both sides planned to target random neutrals have no real evidence behind them and they don't make any strategic sense. Why waste bombs on Peru or Uganda? What purpose does that actually serve? Even after Russia and the US have nuked each other to slag, these third states are not military threats - Chile isn't going to invade Russia, for goodness sake. Especially since the US, and I would suspect the Russians, planned to retain a portion of their arsenal as a post-exchange reserve. And if you've nuked them, you can't trade with them for food to feed the starving remnants of your people, or fuel to keep what's left of the transport net running. There's no upside to attacking the neutral states.