This was helpful, thanks. It sounds like radiation levels faded relatively quickly after the bombing. From your link:
These calculations showed that the highest dosage which would have been received from persistent radioactivity at Hiroshima was between 6 and 25 roentgens of gamma radiation; the highest in the Nagasaki Area was between 30 and 110 roentgens of gamma radiation. The latter figure does not refer to the city itself, but to a localized area in the Nishiyama District. In interpreting these findings it must be understood that to get these dosages, one would have had to remain at the point of highest radioactivity for 6 weeks continuously, from the first hour after the bombing. It is apparent therefore that insofar as could be determined at Hiroshima and Nagasaki, the residual radiation alone could not have been detrimental to the health of persons entering and living in the bombed areas after the explosion.
This page has a table indicating that doses up to 100 rem can cause a temporary reduction in white blood cells, and an increased risk of cancer later in life. But beyond that, not much. So if you lived in Hiroshima/Nagasaki but were out of town on business when the bombs hit, you were probably fine even if you came home later that day.
The rapid reduction of ambient radiation levels after the bombing is consistent with what I found on a website maintained by the city of Hiroshima:
Research has indicated that 24 hours after the bombing the quantity of residual radiation a person would receive at the hypocenter would be 1/1000th of the quantity received immediately following the explosion. A week later, it would be 1/1,000,000th. Thus, residual radiation declined rapidly.