The world has ended as we know it blah blah..we've all watched Mad Max 2
There is no Petroleum products.
Were's the best place to locate our community..on a hill? on a river? by the sea?
Not to beat on you too much Polly, but this is unrealistic. There will always be "petroleum products" of some sort. First of all, there is lots and lots of stored oil around the globe and there is a fair amount of refined fuel laying about as well. I'm trying to envision a scenario where it all goes "poof" suddenly. I can't. Oil and fuel will not be the immediate concern - certainly not in the first fews days after the world ending event. But it will be in short order and the people with the fuel will control much of the future of the world. Sorta like today, but just more acutely.
Also, it depends on what happened. If the people just died off in a global plague or were killed by hordes of Zombies like in the Walking Dead - most of the infrastructure and machinery would still be in place. The oil wells, the oil and gas storage, the cars, the airplanes, the power-plants, electrical grid, etc. OTOH, if it was messy like in a large scale nookaler war - then that's a different story.
The bottomline is your hypothetical needs a lot more detail in order to properly answer the question. What caused the apocalypse, how many people are left, what infrastructure - if any is left, what dangers to human survival - other than natural/climate - still exist, etc?
You're Haven't thought about the mutant unicorns and the virus filled fairy dust that smells of strawberries squirted from their horns.
This should be your real concern.