You're starting your question from the wrong end.

Hiroshima and Nagasaki were the last cities destroyed. The conventional bombing and firebombing of Japanese cities had already either destroyed or done significant damage to 68 other cities. More people were killed in one night in the firebombing of Tokyo than were killed outright by either atomic bomb (if you include deaths from radiation that happened after Japan surrendered, Hiroshima and Tokyo are more comparable). In general terms, more than 1,000,000 people died from non-nuclear aerial bombardment, whereas about 150,000 died in both atomic attacks before Japan surrendered (~225,000 had died by by December 1945). For people living outside of Hiroshima and Nagasaki, the atomic bombs were just another headline that another city had been destroyed.

That is to say, many cities had already shut down. People had already fled to the countryside on scales much larger than those that fled the atomic bombings. More than that, people had already been on near starvation rations for the final months of the war, and there really was no normal daily life by the time the atomic bombs were dropped.

It is also worth noting that most people in Japan did not really understand what an atomic bomb was. On top of that, the wartime government suppressed information about the extent of the damage, as did the US occupation afterwards. Shortly after the bombings and Soviet declarations of war brought about Japanese surrender, most people were concerned with their own misery and the high price of food on the black market. Hiroshima and Nagasaki did not become hot button issues in the national psyche until they were rediscovered after the Lucky dragon incident, when some Japanese fishermen were accidentally irradiated by the Bikini atoll H-Bomb test.

The fallout from Hiroshima and Nagasaki wasn't really a widespread issue. People in Hiroshima were moving back into the bombed area within weeks (The newspaper was back up and running 3 days after). As a comparison, If you look at the number of bombs detonated, the US South-West has experienced far more atomic bombings than Japan, and you don't really hear Albuquerque raising that much of a fuss about fallout (Here's an interesting visual representation of global nuclear explosions). The worst of the fallout from nuclear bombs dissipates relatively quickly and doesn't spread all that far from the site of the explosion.

If you want a good account of everyday life immediately after surrender, look at John Dower's Embracing Defeat.