We can point to things people said and did in the past and make informed judgements about the plausibility of various reasons they had for doing what they did, but again: anyone who asserts bluntly and with confidence that "Japan would have surrendered if..." or "Japan did surrender because..." isn't helping.

Japan surrendered after Nagasaki was bombed. Some people think this shows that Hiroshima alone was not enough to convince the Japanese government that the new weapon would turn the tide of war against them.

Russia declared war on Japan after Hiroshima was bombed. Some people think this was important to Japan's surrender, but would it have happened without the bomb?

Japan had a history of fighting for every inch of territory. Some people think a conventional invasion would have resulted in a rapid conquest.

Area bombing in Europe had a relatively small effect on the Axis war effort, and an awareness of this was growing within the Allied command. Within military circles there tends to be a feeling that if something isn't working the best thing is to do more of it. The bomb was more of it. Thus, the ineffectiveness of area bombing in Europe may have contributed to the decision to use the bomb in Japan.

And so on...

It is worth noting that war itself is almost always strongly motivated by counter-factuals. "If we just bomb the enemy they will surrender" (they don't: they become more dogged in defense until they demonstrably face total destruction). "If we engage in horrific acts of terrorism the enemy will run in fear!" (they don't: terrorist organizations that employ violence against civilians have a zero--yes, zero--rate of effectiveness in achieving their goals: http://belfercenter.ksg.harvard.edu/publication/792/why_terr...)

All we can say with anything remotely resembling certainty was that the bombs did drop and the war did end. We can make some informed guesses about why both sides decided the way they did. We can say virtually nothing with any certainty at all about what would have happened if any major decision had been different... except maybe one.

What if Japan had never attacked Pearl Harbor? This is a counter-factual that people who are wont to make blunt, confident predictions about "what would have happened" had the Allies never destroyed Hiroshima or Nagasaki are generally surprisingly silent about, yet it is one of the few things that would plausibly (not certainly) have avoided the subsequent destruction of those cities.