I lived in Japan for six months where I stayed in Aizu, which is in Fukushima, and it was directly after the disaster (Although I was there for different reasons). The bombs that fell on Hiroshima and Nagasaki were something I learned about when I was young because my grandfather was on the USS South Dakota, a battleship that fought in the Pacific theater. Obviously this has sort of shaped my views.
I later looked at which cities were bombed by my grandfather's ship and met some people whose relatives also fought in World War II, so that gave me a bit more perspective, but it's still something that is very hard to judge.
In looking at raw destruction, the Dresden firebombing was more destructive and more lethal. One thing that differentiates this attack was that it was mainly aimed at civilians.
The world had spent several years waiting for the Axis powers to be start being peaceful. Suggesting that everyone should have just sat and waited for them to stop waging war goes well beyond ignoring reality.
[Edit changed "murdered" to "killed" to make it less inflammatory]
Culturally at the time there was a sort of head down stubborn attitude in Japan. Finding a solution to ending the conflict that fit within the scale of the violence would still be difficult, but it's hard to consider atomic weapons as the only way to end it.
Hindsight is always 20/20. In this case not really. There's no way to know 100% what would have happened, all we know is what did happen.
History's been my thing since, oh, the early 70s, and in the last half decade I've been closely studying WWII history, especially in the Pacific, and the Manhattan Project in general in the last half year or so. Nothing I've come across suggests there was any better option, if you accept the targeting of mixed use civilian-industrial areas.
Operation Olympic, the invasion of Kyushu, was toast as originally planned, too many IJA ground reinforcements, and our estimate of the number of Kamikazes was low, actually 8,000 or so (!). Thanks to the latter, the Battle of Okinawa was the most costly in US naval history, and it would have been much worse with their not having to fly so far let alone over the featureless ocean.
Those who knew about the Manhattan Project were planning on using 5-8 bombs to make Olympic feasible, and per the above linked book, there was major discussion about what to do with the 3rd bomb if the 2nd didn't force a surrender.
Those who didn't know were planning on mass use of chemical weapons....
The Soviets wouldn't have been much help, if ever, in taking the home islands (who's navy would land them even if they were willing?), but it didn't hurt how they predictably smashed through the IJA in China when they got started between the two bombs.
Just letting them starve on the home islands ... very bad, and again, costing a quarter million lives a month in the sphere outside of the home islands. East Asia was already enough of an abattoir, 25 million plus lives lost.
As for concessions, besides the fact that we'd pledged "unconditional surrender", which we indeed backed off of for the Emperor, I'm just not aware of what specific concessions we could have made that would have likely made a difference. Especially since unconditional surrender was part of a "never again" post-WWI attitude (per Tom Lehrer's MLF Lullaby "We taught them a lesson in 1918, and they've hardly bothered us since then") we were very determined that we wouldn't have to do this again. And, you know, we succeeded, and as I've noted in a previous recent A-bombing discussion, we've not had another great powers war since then.
Anyway, I just wanted to share my unique perspective and experiences without getting down voted, and I've already lost 2 karma on this discussion.
If you have an interest in the country's culture more than its military history (or modern military history) you might enjoy some of Alex Kerr's writing, either Lost Japan or Dogs and Demons.
Relevant because this article gives perspectives from around the world, all of which are interesting.
Ultimately, though, I feel this is an event in history that relies upon the mutual feelings of Japan and the United States.
There weren't really all that many ways it would end given that the Soviet Union operated independently and was in a position to invade much earlier.
Ichi-go Ichi-e, 一期一会, is a 16th century Japanese phrase saying that we meet each other only once in a lifetime. (Opportunities are scarce.)
And then there are the stories of the three samurai and the songbird.
The samurai are Nobunaga, Hideyoshi, and Ieyasu.
Each of them encounters a songbird and wishes to hear it sing.
Nobunaga says, if you do not sing for me, then I will kill you. And he takes out his sword to slice the bird.
Hideyoshi says, if you do not sing for me, then I will make you sing. Then he offers the songbird something sweet.
Ieyasu sees the bird and says, if you do not sing for me, then I will wait until you do sing. He then sits and waits (forever).
There were many ways the allies could have ended World War II in the Pacific theater. The United States, with the dropping of the atomic bomb, chose to follow Oda Nobunaga's philosophy. Whether that is right or wrong is its own debate.
The philosophy of the 16th century samurai is a big thing in Japanese culture and often an interview question for candidates applying at a company. I have a limited knowledge of the samurai from visiting Nisshinkan in Aizu when I lived there. That was a samurai school where young fighters trained who fought in the civil war.