In almost every way I can think of, distributed monetary systems would be superior to centralized monetary systems.
Any centralized transaction processing facilities i.e. banks in these cities would be destroyed however distributed transaction processing would fare much better since it would not rely on a single node to function.
The other thing worth considering is the value of the currency for any of the countries on that list if they chose the wrong ally and ended up on the losing side. Their currency would most likely be devalued beyond repair.
This question really is about comparing Bitcoin as a value store to something like Gold not a fiat currency. It occurred to me that even were Bitcoin to survive and thrive for the next ten years, growing in infrastructure and adoption, that the ultra planner types would always want to store a substantial portion of their assets in Gold to protect against the worst of disasters. Bitcoin is not really designed to survive a worst case scenario. However, Gold is..... IMHO
I think the most valuable things in the scenario your talking about is bullets and fuel in order to procure water, food and shelter. I don't think gold will be worth much however, if it was simply a world war 3 scenario then ya I think gold is a good idea.