The conclusion about the dead places is that they were part of New York city which had been destroyed by some kind of weapon of mass destruction. This weapon left some kind of poisonous residue that made it impossible for men to enter the city for a long while. ( Many readers believe the residue was caused by an atomic bomb. However, the story was published eight years before the bomb was developed and detonated.)
After John has survived his journey though the dead places, it is apparent that the city is probably safe to visit. So John decides he can go back, read the books, gain the knowledge the New Yorkers possessed and teach it to his people. This is not a particularly good omen because John's society is likely just a susceptible to "eating knowledge too fast" as the previous society. Thus, the story is a warning against developing weapons that can destroy society before developing methods to contain those weapons.