I would say their war tactics and public statements leading up to the nuclear bombings would suggest that surrender wasn't in high regard with the people that counted. Especially among a military with a warrior mentality where surrender was considered shameful. These were people, including civilians, that would throw themselves off of cliffs to avoid capture.
The US military warned the populace numerous times that their cities would be firebombed. I would assume this was an effort to push towards surrender. Why else warn them? No surrender.
Before the first bombing the Japanese government was told to surrender. No surrender.
After the first bombing, a demand to surrender was made. No surrender.
The second bombing and another demand to surrender. Around five days later the Emperor finally told the people of Japan that surrender was necessary. Know why it was almost a week later, even though they were told more were coming? Because the Emperor wanted to stay Emperor.
That's the part that people don't seem to understand. The nuclear bombings were not intended to convince the Japanese populace to surrender, because many might have on their own without the bombings. Even many in the military might have been willing to surrender. It is said that Yamamoto despaired attacking America from the beginning. But more than likely, none of them would have surrendered until the Emperor told them to do so. In the end, the nuclear bombs were to convince the Emperor to surrender, not the people. Even facing this threat of total destruction he still held out for his own selfish reasons, and even then claimed he was doing it to save mankind. The simple fact this statement of saving mankind came from a military leader who's policy seemed to be maim, torture, and kill anyone that wasn't Japanese is one of the most brazen attempts at spin that's ever been tried.
Never mind the fact that the Soviets were ready and willing to invade. You can ask the Germans how that went for them.
Now, I've heard of this thought that there are examples of the Japanese willing to come to a peace agreement. But suing for peace is a different matter than total surrender. Peace agreements with the aggressor often have a problem of leading to future conflicts when the peace agreement no longer holds true. Ask the Koreans how they feel about their "peace agreement" with the never-ending threat of war, as comical as it may seem.
Think of the times; America had suffered huge losses in men and wealth to fight two massive fronts in a war they didn't start. Don't forget the millions, I'll say it again, MILLIONS, of people that died at the hands of the Germans and Japanese. The war in Europe was mostly over and the only reason for that is because Hitler was dead, many Germans fought to the bitter end even though it was obvious they were going to lose. No one wanted a repeat of the ending days of the European theater in Japan. The people around the world wanted that crap to end as soon as possible. You have to understand that the Allies at this point had built up such hatred for the Japanese that many would not have a problem whatsoever invading and killing every man, woman, and child of that small island nation. It would have cost dearly to do so, but it would have been done. The likely outcome is that the Japanese people would have become the human equivalent of an endangered species.
So all this talk of they could have done this, they could have done that, or whatever else all has the benefit of seriously strong hindsight.
I agree, nuclear weapons were not needed to end the war, but considering the other options, it was probably the best choice at the time.