As I said earlier I shouldn't think a nuclear war would manage to kill everyone.
There have been numerous cataustrophic events and life is still here - humans were down to a few thousand individuals 30,000 years ago
http://content.usatod...urope-/1#.T31G_NUrImA
What sort of world would they inhabit? Well probaby a tough one - but civilisations would doubtlessly rise again.
I doubt they'd be as technologically sophisticated as us though.
We've used all the metal ore and raw materials in easy reach of the Earth's surface