I've done some research, and there are many great books about the rebuilding efforts post WWII.
My question is, wouldn't there be nuclear fallout and radiation that would prevent rebuilding for many many years?
The short answer to the fallout question is "no." Dangers from nuclear fallout and radiation are generally greatly exaggerated in the first place, and the Hiroshima and Nagasaki bombs were not particularly "dirty." Furthermore, there was little understanding of radiation, probably very few radiation detectors, and a city that needed rebuilding.
A major factor determining fallout from nuclear weapons is whether it explodes up in the air or close to ground. In the former case, the nuclear fireball does not touch the ground, and the only things close to bomb that become radioactive are parts of the bomb, the fission products of the explosion, and whatever there is in the air to be activated by neutrons released in the chain reaction. While there are some elements in the air that become radioactive, most of these are very short-lived, lightweight or inert, meaning that they tend to decay and dissipate to harmless levels fairly rapidly. As a result, most of the fallout in an "airburst" consists of actual vaporized particles from the bomb itself. Both Hiroshima and Nagasaki, where airbursts were used to maximize blast effects, received such fallout in form of rain soon after the bomb exploded, and while this fallout likely caused some long-term medical effects primarily among those who happened to be outside as it fell (or drank contaminated water), it was not sufficient to cause a long-term hazard. Once short-lived and therefore more dangerous radioactive elements had decayed, risks from this type of fallout are not distinguishable from health risks caused by natural background radiation. The Radiation Effects Research Foundation, which studies the long-term effects of Hiroshima and Nagasaki, estimates that almost 80% of the theoretical maximum cumulative radiation dose would have been delivered within one day of the bombing, and only 10% after day 6. Today, residual radioactivity due to bombings cannot be reliably distinguished from trace radioactivity that's present everywhere on Earth due to nuclear bomb tests in 1950s and 1960s.
However, were a bomb to be exploded so close to ground that its fireball touches the ground itself (to destroy buried structures for example), neutrons have much more material to activate, and the fireball will sweep much of this heavier material up in the air. This results to much more radioactive fallout concentrated on a much denser area, and can result to lethal levels of fallout.
The definitive and ongoing study of the radiation effects on Hiroshima and Nagasaki is by the aforementioned Radiation Effects Research Foundation, which discusses this topic here: