Denver has a few things going for it. It has proximity to amazing shale-oil reserves, meaning there will always be fuel.
In the event of a war it's the easiest city in the US to defend, as it's a mile above sea level (and nowhere near the sea) and surrounded by mountains.
Its elevation also makes it an excellent place to go in the event of global warming. In fact, global warming should help make Denver's surrounding agricultural land incredibly fertile.
Antarctica is probably one of the most inhospitable places in the world, and that's why it's the perfect spot to hide out come the end of the world. If you can manage to get there with enough food to survive the cold winter, you can base yourself in one of the expedition huts and hunker down until things improve. War is unlikely to ever reach the world's southernmost place.
The only downside is that if sea levels rise because of climate change, you might end up like this penguin.
This mountainous region of Indonesia wouldn't seem like a very hospitable place to live. But then, remember, in a time like this you're not exactly looking for hospitable. You're looking for survivable. And it turns out that the largest gold mine in the world is in Puncak Jaya, which means there could be tons of work and trade if you play your cards correctly. It also houses the third-largest copper mine on earth.
When you're in the land of Africa, Cape Town is as good as it gets. With gorgeous views and harbors, the city is the second-most populous in South Africa with good reason. Even if everything went horribly wrong, Cape Town would quietly continue along, as if nothing had ever happened.
The state of Cape Town's economy is nothing like that of its sister cities to the north, thanks in part to the location of South Africa. It also is relatively free of Western foreign influence.
Switzerland has undoubtedly proved itself a haven during Europe's bloody past.
Bern is surrounded by the Swiss Alps, giving it natural protection, and the Swiss capital is probably the best place to hide out in Europe thanks to its diplomatic nous.
Switzerland is known for having remained neutral in every major conflict in the past few hundred years, and this neutrality makes Bern a pretty good place to hole up during World War III. Swiss agricultural land is already some of the most fertile around, and this will only get better if climate change starts to really hit home.
Bern is believed to be named, conveniently, after the German plural for bear, "Bären." It even has a 500-year-old tradition of maintaining live bear pits, and now a more humane bear park.