The fallout decay rates they published in the old civil defense manuals assume that a nuclear detonation is taking place in a large field of pure silica - sand, as all the groundburst nuclear tests were staged. The results are for "unsullied" bursts that vaporize sand into glass and superheated silicon gases.
The problem is that in real life there is no such thing as an "unsullied" nuclear burst conducted near ground level.
In any metropolitan city there are a million contaminants which could extend the radioactive half-life from weeks to decades. You will find cobalt (used widely in industry and medicine) cesium, precursors of americium and many other pollutants inside the fireball that will not wane for many moons. Depending on wind distribution and airflow patterns you might have areas that remained unsafe a half a century out.
Of course, all this is also based on the naive assumption that the nation using the weapon did not deliberately salt the warhead to maximize it's radioactive yield to begin with. Vault-Co promises you that this is highly unlikely during a nuclear war, despite whatever some game theory academic may have postulated previously.