I don't know if it was wrong or right to use the bomb on Hiroshima...but I believe that the Nagasaki bombing wasn't needed at all.
I can understand that given the almost fanatical resistance that the Japanese military were showing, despite being regarded as being a beaten force, bringing the Pacific war to a swift end by dropping 'Little Boy' was perhaps a wise move.
There was no real way of knowing how many more lives could have been lost through conventional warfare by delaying the use of the bomb, and after bombing about another 60 japanese cities to dust with conventional bombs, there was obviously no moral problem for the Americans.

More than anything else though, the decision to use 'The Bomb' was based on justifying the huge cost spent on the Manhatten project....but more importantly it was to send a message to the Soviets who were already looking to the future after the war.
That's probably why the 2nd bomb was dropped...to show Stalin that the 1st wasn't a fluke.
As usual lives were lost to play the political game.