Here is something I cut + pasted from another site:
The Target Committee at Los Alamos on May 10?11, 1945, recommended Kyoto, Hiroshima, Yokohama, and the arsenal at Kokura as possible targets. The committee rejected the use of the weapon against a strictly military objective because of the chance of missing a small target not surrounded by a larger urban area. The psychological effects on Japan were of great importance to the committee members. They also agreed that the initial use of the weapon should be sufficiently spectacular for its importance to be internationally recognized. The committee felt Kyoto, as an intellectual center of Japan, had a population "better able to appreciate the significance of the weapon." Hiroshima was chosen because of its large size, its being "an important army depot" and the potential that the bomb would cause greater destruction because the city was surrounded by hills which would have a "focusing effect".
Secretary of War Henry L. Stimson struck Kyoto from the list because of its cultural significance, over the objections of General Leslie Groves, head of the Manhattan Project. According to Professor Edwin O. Reischauer, Stimson "had known and admired Kyoto ever since his honeymoon there several decades earlier." On July 25 General Carl Spaatz was ordered to bomb one of the targets: Hiroshima, Kokura, Niigata, or Nagasaki as soon after August 3 as weather permitted and the remaining cities as additional weapons became available.
it wou8ld appear that the decision was made on either 10th or 11th May 1945