I think the one thing everyone can agree on is that this question is a heated topic, and the only answer is the one that you feel is right. Going under the aforementioned assumption I bring this to the table, and I apologize if someone has already stated this:
The Honorable Emperor Showa, the 124th Emperor of Japan, the Son of Heaven, was told before the first bombing: "the inevitable and complete destruction of the Japanese armed forces and just as inevitably the utter devastation of the Japanese homeland". Basically The US warned Emperor Showa that they would utterly destroy them if he did not surrender. Emperor Showa responded by keeping silent and taking no action, a kind of "Silent Kill", almost to the point of ignoring the threat; however, Emperor Showa did send orders to his Advisor, Koichi Kido, to make The Imperial Regalia of Japan safe at all cost. Before the first bomb caused cataclysmic devastation, one of the three pieces of The Imperial Regalia of Japan was moved out of Hiroshima to an undisclosed location. This shows that The Honorable Emperor Showa knew, or at least had an idea of where the first bomb would land and he did nothing to save his people.
Now, before I go on, please allow me to explain. I am in no way condemning or condoning Emperor Showa's actions or inactions. I am merely stating what is widely accepted as fact and true.
Now for those of you who do not know the accepted belief behind The Imperial Regalia of Japan, they are three sacred treasures; each of them represents the very birth of Japan as a nation. However, there are numerous copies of these treasures and no one is allowed, save for the Emperor and those he trust above and beyond all things, where the real treasures are located. The one moved from Hiroshima could have been simply a fake treasure, or it could have been real, I don't think that is a relevant point for the question; but it does illustrate an idea. If they were concerned with moving a copy of a sacred treasure and not concerned with moving innocent civilians, what does that mean?
There are many possibilities, and I make this point to only show that the US was not alone in the tragedy that befell Hiroshima.
On the topic of the second bomb; After Hiroshima suffered a hell on earth, Emperor Showa and his war council did not believe that the Americans had a second bomb of that power. It is an understandable belief, someone shows off their biggest and strongest weapon to only scare their enemies into surrender, and their enemies later discover that the weapon was a one time deal. It is a tactic that is used very often, even in everyday life; except without all the death. The second bombing proved to Japan that indeed, the Americans could cause such destruction a second time; at which time Emperor Showa could do nothing but surrender as an honorable and brave leader of his people.
Now to shed a little light on the true evil of the bombings: The targets were selected through a truly evil series of requirements. The targets needed to be heavily developed, buildings, people, businesses, major roads, etc. The targets needed to have been free from attacks before hand, a kind of untouched by lesser bombs idea, and larger than 3 miles in diameter and important targets in a large urban area. The targets were selected strictly to see just how much devastation one bomb could cause, so the Americans could watch from afar and see the fruits of their testing could provide. To me that is the stomach turning and truly disturbing aspect of the bombings. The targets were chosen because that is where the most death would be caused.
It was a dark and nightmarish chapter in the history of the world, a history that is a catalogue of death and violence, and I personally hope that such a level of destruction is never reached again.
Now please, think of this. After the surrender and Japan was forced to de-militarize, the Nation of Japan put all their energy into developing peace time technology. The Nation of Japan became a powerhouse of technological advancements and education, they flourished and the tiny Island Nation reached something that most tiny island Nations could only dream. They became a world power in The World Economy.
In closing and to restate, the bombings were a part of our history as a world. A dark and nightmarish part that should never be repeated, but it opened the doors for a new world. I must apologize profusely now; I apologize for not answering the question and giving this lengthy and wordy writing about many side notes to add to the debate. I believe that the bombings were sadly made necessary, due to the actions that led up to the bombings. There is no excuse for the untold destruction caused by war, ever; but until everyone on this world can reach peaceful resolutions in regards to all things, war will be a dark and sad constant and in war death is necessary. A Leader of a Nation does not listen to 100 soldiers killed, a Leader of a Nation listens to 1,000 civilians killed, and that fact saddens me to my core.