For the record, the Allies wanted unconditional surrender because of a little failure called the Treaty of Versailles. If you don't what that is, then you're an idiot because it's extremely relevant when talking about WWII. The Treaty of Versailles is arguably one of, if not, the biggest causes of the Second World War ? especially for the Germans. It taught the world a few things, that kicking a nation when it's down and treating it like it's completely to blame is a bad idea; why do you think Hitler was so popular? Aside from his charisma, he was promising to avenge the wrongs that were perceived to have been done against Germany and restore it to its former glory.
Aside from that, the Treaty of Versailles also kicked the Italians and the Japanese pretty hard. Both of them joined the war and expected to be given some sort of territorial award for their services. Of course, that didn't happen. They didn't get the areas that they wanted and left skulking as Germany's colonies were divided up amongst France and the United Kingdom for the most part.
As for the Americans, we get from then president Woodrow Wilson, his Fourteen Points on which the League of Nations was founded. Think of it as the precursor to today's United Nations. It basically was a diplomatic forum for countries to solve dispute between them through mediation. Which didn't work so well because neither Britain or France was willing to stick it up and actually back any of the resolutions passed which let the Italians and the Japanese skate by with their conquests in the run-up to the Second World War. Same thing happened with Germany. Remember Czechoslovakia? It was the one country that had an organized military and was actually a sort of bastion of Western thought in eastern Europe. Of course, Czechoslovakia was a conglomerate of various nationalities, including the Sudetenland which was comprised of Germans. That didn't make Hitler too happy and it took only a little effort of throwing his weight around and making some threats about armed conflict that made France and Britain bow to his wishes.
Hence why we have Chamberlain going on about a piece of paper bearing Hitler's signature and how he averted a war. Good job there sir.
In any case, I'm getting really off topic here...
While today we really wouldn't approve of dropping atomic weapons on cities filled with civilians ? but we still seem to have no problem with bombing areas that are known to have civilians in them, albeit not using atomic weaponry ? considering the time period and the frame of mind of most Japanese citizens it could be considered a necessary evil.
Forecasted casualties for an invasion of the Japanese islands was extremely high, in excess of a million American soldiers ? someone stated the statistics on an earlier page ? and that loss of life was considered to be greater than the damage caused by dropping an atomic bomb on a city. Dropping two, though, might be overkill, especially since there wasn't really a reasonable time period between the two dates. Hiroshima was bombed on the sixth of August, with Nagasaki bombed three days later on the ninth. I would have to say that maybe if the Japanese government had been given a little more time, the faction arguing for surrender would have been able to secure it; especially when the casualty rates and damage had been calculated to a more accurate degree.
However, a lot of this is mere speculation. But given the Japanese mentality, it isn't surprising that extreme measures had to be resorted to. It's similar to what happened in Germany; a lot of propaganda supporting that it was better to die in battle than to surrender and bring shame upon your nation. Both the Germans and the Japanese were subjected to a sort of brainwashing that can also be seen being utilized by Soviet Russia. The glorification of the leader to almost divine or prophetic levels, and the idea that serving them and your country loyally is the greatest honor that one can do. The brainwashing was effective; just listen to testimony given by survivors or people who lived through that time period.
Reasons for the Allies wanting a unconditional surrender: Because they were thinking of Versailles and also because they hadn't negotiated things out completely with the Russians, aka Stalin. Note that this might not be completely accurate, but from what I remember its mostly the case. There's other factors too.
Also, I'm directing this at TeeBs: How about you go Google Hiroshima and Nagasaki in accordance with 'atomic bomb' or any variation of that. Go and see what happened to the survivors or people who escaped. You obviously don't know what radiation can do or the grievous injuries that are caused by exposure to that. Radiation causes heat, heat burns. The heat from the bombs burned the patterns of women's kimonos into their skin. I'd post images but I don't think anyone but you deserves the horrors of having to see them.
This is, again, a case of whether or not the means justify the ends.