When the time came to decide whether to use the A-Bomb, the Allies had already fire-bombed Dreseden and Tokyo, and if you haven't read about the horrific loss of life those bombing raids caused, then you can't begin to understand the decision-making process that led to dropping the A-Bomb.
World War II was not like any war any of us on these forums have participated in or seen on TV. World War II was total war, and civilians were simply not off limits to either side. Both the Allies and the Axis had made it clear that conditional armistice was not an option.
With their banzai charges and suicide-over-surrender behavior, the Japanese were telling the Allies that they were fully prepared to fight to the death against the West. The Allies called their bluff by proving they actually *were* willing to kill every last Japanese person on the islands in order to win. It was only when faced with an actual choice of surrender or genocide of the entire Japanese race that the Emperor chose surrender.
The atomic bomb was not inherently necessary for the Japanese to be convinced of their imminent annihilation. The Allies were, in fact, willing to destroy Japan, and were doing a good job of it with fire-bombing using thousands of bombers, well before the A-Bomb got dropped.
The A-Bomb was just a quicker and easier method of achieving the same goal as the fire-bombing. It let us make it look easy, suggesting we could casually wipe our enemies out of existence. (And it wasn't racial. We fire-bombed Germany too, and we developed the A-Bomb to use on them, initially). That's the context in which the decision was made: Having already decided we might have to wipe everybody out, we decided to show we could do so pretty fast, hoping they'd surrender and we wouldn't have to.
So, really, "should the A-Bomb have been dropped" is the wrong question to ask. The right questions to ask are:
1) Was unconditional victory so important that the Allies should have been willing to inflict massive civilian death? i.e. was "strategic bombing" necessary
2) If so, was using a new weapon that made inflicting massive civilian death faster and better the right decision?
You have to look to your own morality to answer question #1, but if you say "yes" to it, it's hard to say that using the A-Bomb was wrong. In short, if you want to criticize the A-Bomb, criticize strategic bombing as a whole.
(For more details on the above line of thought, check out the excellent book "Japan's War", by Edwin Hoyt, which traces the course of World War II from the Japanese perspective.)