Not to discourage further discussion, but you might be interested in these posts from the FAQ:

• Did the US have to nuke Japan in WWII?

• Would the Japanese have likely agreed to total unconditional surrender after just a "warning shot" pf the atomic bomb?

• FAQ section on the atom bombings

There were people on the Manhattan Project who advocated a "demonstration" for the first use of the bomb. They didn't win out. I have written about this argument here.

The very first proposed target for the bomb, in 1943, was Chuuk Lagoon, basically the Japanese equivalent of Pearl Harbor, an almost entirely military installation. By 1945 it was no longer a target and US targeting strategy had turned to focus on destroying entire cities. If you read the Target Committee meeting of May 1945 you can see how their philosophy had changed by then. They were interested in the bomb making a psychological statement, and for that they wanted to showcase how destructive it was, and for them that meant destroying an entire city, preferably one that had not been bombed much until that point.

I did a paper or two on this, so I hope I'm not talking totally out of my bum. Keep in mind, neither Nagasaki nor Hiroshima were just civilian targets--both were home to large and important military installations. There was also a question of economy-at the time of the Hiroshima bombing, the US had perhaps nine atomic bombs. If they didnt succeed in cowing the Japanese, then that would be a waste of a bomb. (It took two before the Japanese surrendered, and it was still close--half the Japanese cabinet was in favor of continuing to fight. So it wasn't an unjustified fear.)

There's also speculation that it was intended as a demonstration of power to the USSR to the USSR.

On mobile, will add sauce later.