I think the discourse around the use of nuclear weapons in Japan in WW2 is in some ways a bit unfair. It's so easy to look back with the benefit of hindsight and judge the decisions that past people made, without appreciating the information that they were operating on and the context of the time. I think as a student of history, you often find that historical person were smarter and more reasonable than they are given credit for, given the information and incentives that they were operating on.
When we talk about a negotiated settlement, it is important to consider the context. World War 2 started in part because the negotiated settlement of World War 1 allowed the Nazis (and to a lesser extent, Japan) to sell the message that the military had not been defeated and were instead stabbed in the back during political negotiations. Japan was saying that they only wanted the imperial household to retain control, but it is hard to imagine them accepting the loss of Korea, Taiwan and Manchuria - let alone the pacifist constitution that was imposed on them. But even with the benefit of hindsight, it is not hard to imagine that anything less than an obvious and total defeat of the Japanese military would have led to a third world war as soon as the US was distracted by the USSR and Japan developed its own bomb. If Communist China could do it by 1964, Japan could have done it much more quickly.
But more broadly, from US' perspective, the reality is that the US didn't know whether Japan would accept an unconditional surrender or not without the use of the bomb. They didn't know if Japan would surrender or not even after the bombs had been dropped.
Modern observers also need to consider the context of the bloodiest war ever fought. The harsh calculus is that 50M people had already died and every week hundreds of thousands of people in China were dying between the Guangxi campaign and the invasion of Manchuria, thousands were dying in the firebombings in Japan, and on top of that the US faced the prospect on an invasion of the home islands in which millions would die.
In that context, dropping two bombs in which only tens of thousands of people would die must have seemed like a clean ending to the war. In the end, the atomic bombs killed 150,000 people. You should also remember that Hiroshima was not a major population center, and neither was Kokura - the original target of the Fat Man bomb. The plan was to solely target military targets as both a show of force, to ease a potential land invasion, and to avoid using weapons of mass destruction against population centers. Nagasaki became a target only because Kokura was under cloud cover and the pilot made the field decision to either bomb a secondary target or risk being shot down and losing the bomb.
I think if any of us had been in the same position, it is hard to argue that we would have chosen differently, and it is harder still to argue that choosing differently was clearly the right choice. And if that's the case, it hardly seems fair to judge people in the past for making that choice.