The two bombs dropped on Japan were rather "clean" as far as fallout goes... Let me explain.

What we commonly call "fallout" is generally caused when the bomb's fireball touches the ground (a "surface burst"). It turns vast amount of earth or water into a fine particulate matter (nanometer size and up) that gets heavily irradiated by the explosion, then sucked up into the mushroom cloud. Much of this material will fall from the fireball or the "stem" of the cloud rapidly, while the rest will make it up into the stratosphere and spread downwind. That which falls out of the fireball or the stem will heavily contaminate the local area of the detonation.

The two bombs used against Japan, however, were airbursts, not surface bursts, exploding about 1900 feet (Hiroshima) and 1700 feet (Nagasaki) above the cities, to cause maximum blast damage. Their fireballs never came close to the ground, so the only material they could turn into fallout was that already in the air... mainly the metals of the bomb itself. While this did generate fallout, to be sure, there would be much less of it spread over a larger area.

An area contaminated by fallout will (generally) be safe to travel through within a month or so.

As far as Hiroshima and Nagasaki went, the long-term damage from fallout was, on the whole, less than the damage caused by the immediate radiation release from the bomb, the thermal effects, or the blast effects. Within a month, there was little residual radiation left over from the bomb at Hiroshima. Don't get me wrong, people were still dying from radiation sickness, but much of that was from the initial explosion, not fallout-caused. Likewise, long-term cancers, birth defects, and so on were probably caused by the initial dosages from the bomb.

Not to say that fallout isn't damaging and nasty, but there just wasn't all that much of it from the bombs at Hiroshima and Nagasaki.

Going to ping /u/restricteddata, who should be able to answer your question :)