Some other possibilities, as the length of time between the successful testing of the bomb and our actually dropping it was a mere three weeks, and the decision-making process to do so is a little muddled historically.
First, the Manhattan Project was designing a bomb to be dropped on Germany as soon as we developed it. However, we were not able to test one until July 16, 1945, and Germany surrendered on May 7th. The decision to focus on Japan then was a quick one, and with a new President, Harry Truman.
Hiroshima and Nagasaki were not terribly important militarily, but they were two of the only cities not yet bombed, and still mostly intact. We wanted to see the full effect of the atomic bomb on an undamaged city. This lends strength to the argument the bomb was dropped to scare the Soviets as well as to convince Japan to surrender.
Another reason, and I think the most compelling, was out of hatred and revenge. Revenge for the Bataan Death March, for Pearl Harbor, for how our prisoners were treated, for the Kamikaze attacks, etc. There was simply no way our government or military were capable of deciding anything other than using the weapon once we had it.