Here is the Chairman of the wartime Joint Chiefs of Staff, Admiral William D. Leahy:
It is my opinion that the use of the barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender....
Bomb is the wrong word to use for this new weapon. It is not a bomb. It is not an explosive. It is a poisonous thing that kills people by its deadly radioactive reaction, more than by the explosive force it develops.
My own feeling is that in being the first to use it, we had adopted an ethical standard common to barbarians of the Dark Ages. I was not taught to make war in that fashion, and wars cannot be won by destroying women and children.
One other fact, not mentioned by Admiral Leahy: The second bomb was dropped on Nagasaki only days afterward, before the Japanese even had assimilated what had happened at Hiroshima. They certainly would have surrendered without the necessity of a second bomb.
On a completely different note, one should remember that WWII was a class of warfare known as "Total War."
"Total War" is a separate class of warfare, a conflict of unlimited scope in which a belligerent (Japan, Germany, Italy) engages in a mobilization of all available resources at their disposal, in order to entirely destroy their rival & his capacity for resistance. In a total war, there is NO differentiation between combatants and non-combatants (civilians). It views both military and civilians as a single entity.
As a member of the Axis Powers, Japan fought WWII in just such a way - consider it's conquest of China (it attacked the general population as well as its military). And Germany's attack on London & other British civilian centers in what they called the Blitz.
With Hiroshima, it could be said that the US was responding in kind to Japan. Japan did not fight by the Geneva conventions; witness their hideous treatment of the conquered Chinese, horrific medical experiments/attrocities (on a wider scale than Gernany's, and so monstrous, they are almost indescribable), as well as widespread torture of POWs and civilians. (these are things the Japanese commonly 'forget' when talking about the morality of the atomic bombs).
In a war (or battle), the point is to win as quickly as possible, suffering the least amount of losses. It is the application of force, and overwhelming force, if you have it. America had the bomb and it was used to end the war and put an end to American casualties.