Three requirements for being a target were The target was larger than 3 miles in diameter and was an important target in a large urban area. The blast would create effective damage. The target was unlikely to be attacked by August 1945. The initial nominated targets were Kokura, Kyoto, Hiroshima, Niigata and Yokohama. Hiroshima was a major military HQ, a large port and industrial center. It also had an area that greatly enhanced the power of the weapon. Kokura, which was the intended second target, had the largest munition production in Japan. Due to low visibility from smoke and coal fires the bombardier couldn't get a clean visual to drop on Kokura so after the third bombing run with no success and fuel running low they switched targets to Nagasaki the secondary target. Nagasaki was the largest sea port for japan at that time and a large industry for producing war materials.

The Ask Historians FAQ links these two of /u/restricteddata's answers about the choice of targets for the atomic bomb.

The general process, which featured Hiroshima as a top-level possiblity.

The targeting of Nagasaki, as a secondary alternative to Kokura.