- Report produced by the U.S Strategic Bombing Group (employed by Truman) to survey the air attacks on Japan concluded that: 

“Based on a detailed investigation of all the facts and supported by the testimony of the surviving Japanese leaders involved, it is the Survey’s opinion that certainly prior to 31 December 1945 and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated.” - page 52-56 

- Dwight Eisenhower future president and then Supreme Commander of the Allied Forces also said:

“I had been conscious of a feeling of depression and so I voiced to [the then Secretary of War] my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives.” - page 380

- Admiral William Leahy, one of the highest ranking officials in the US army during WW2 wrote of the usage of the bombs:

“It is my opinion that the use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. […] My own feeling was that in being the first to use it, we had adopted an ethical standard common to the barbarians of the Dark Ages. I was not taught to make war in that fashion, and wars cannot be won by destroying women and children.” - page 441

- General Douglas McArthur, another high ranking US official in the war:

“[When asked about his opinion on bombing Japan] He replied that he saw no military justification for the dropping of the bomb. The war might have ended weeks earlier, he said, if the United States had agreed, as it later did anyway, to the retention of the institution of the emperor.” - page 70-71

- On September 9, 1945 Admiral William F. Halsey commander of the Third Fleet publicly quoted as saying:

“The first atomic bomb was an unnecessary experiment… . It was a mistake to ever drop it… . [the scientists] had this toy and they wanted to try it out, so they dropped it… . It killed a lot of Japs.” - online source

- The US secretary of war, Henry Stimson, speaking to President Truman:

“I was a little fearful that before we could get ready the Air Force might have Japan so thoroughly bombed out that the new weapon [the atomic bomb] would not have a fair background to show its strength.” - diary of Henry Stimson which can be found online here 

- Even those deploying the bombs questioned the decision to drop them on civilian cities:

“I thought that if we were going to drop the atomic bomb, drop it on the outskirts–say in Tokyo Bay–so that the effects would not be as devastating to the city and the people. I made this suggestion over the phone between the Hiroshima and Nagasaki bombings and I was told to go ahead with our targets.” - online source

- Lewis Strauss Assistant to the Navy Secretary James Forrestal on the locations of the bombings:

“I remember suggesting […] a large forest of cryptomeria trees not far from Tokyo. The cryptomeria tree is the Japanese version of our redwood… I anticipated that a bomb detonated at a suitable height above such a forest… would lay the trees out in windrows from the center of the explosion in all directions as though they were matchsticks, and, of course, set them afire in the center. […] Secretary Forrestal agreed wholeheartedly with the recommendation.” - page 145

So to recap: 

A lot of American generals were against using the bomb as they felt it served an empty purpose.

Those who agreed with its usage completely disagreed with dropping them on cities.

Truman went ahead and had them detonated in two highly populated civilian cities anyway. Two cities that had remained mostly untouched by regular bombings throughout the war precisely bc of their lack of value to the Japanese war effort.  

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