This is an incredibly difficult subject, one that can only be answered with hindsight where we apply the thinking and moralities of today to that of 76 years ago. 70 years ago we weren't living in relative peace compared to now though, we were living under the threat of daily war and bombings from an aggressor who wanted to kill us and so we had to defend ourselves to survive. It's also ironic that we argue against having nuclear weapons whilst living in a time where they cannot be used by an aggressor because we have them.
I don't think that the US should of dropped the bombs but it's easy to apply this thinking when you only consider the destructive potential of nuclear weapons alone. However, remember that the Japanese were not innocent, they started war with the US by bombing Pearl Harbor without warning and they massacred South East Asia and the region.
Certainly the left on this subject point to the UK/US and allies as the antagonists by using nuclear weapons but they fail to refer to history where Japan were responsible for everything that came to them. Germany had already surrendered, they were warned and they refused to comply with requests for peace (Potsdam declaration) even in the face of defeat.
Certainly ask yourself this, would you drop a nuclear weapon on Japan to force the end the war or would you instead send tens of thousands of British soldiers to their certain deaths to fight Japan until they surrendered?