Tokyo was considered a target, but the USA decided that they wanted to induce a surrender rather than kill the Emperor and high ranking military officials. So they decided to demonstrate the bomb's power on the few cities that hadn't been firebombed. Tokyo had already been "bombed and burned out and is practically rubble with only the palace grounds left standing". The target cities were chosen from cities that hadn't been firebombed yet, mainly in the south since that was where an invasion was likely to take place, but also because it would determine how damaging the bombs would be. Many cities in Japan at the time had already been bombed and so that would skew the damage assessment.

As for the targets, Hiroshima was chosen because it was 'an important army depot and port of embarkation in the middle of an urban industrial area. It is a good radar target and it is such a size that a large part of the city could be extensively damaged. There are adjacent hills which are likely to produce a focussing effect which would considerably increase the blast damage." Kyoto was going to be chosen, but the US Secretary of War had his honeymoon there and thought it was culturally significant. As for Nagasaki, it was a secondary target; originally Kokura was the target, but the cloudy weather obscured the view, so the plane turned south for Nagasaki.

A 3rd bomb was being prepared for deployment and its thought that Tokyo was the target, but Japan had surrendered just days before this.

This is a very commonly asked question, and /u/restricteddata has discussed the targeting of the atomic bomb here and here. By this point, Tokyo had already been practically destroyed by conventional firebombing raids, and would not have provided a suitable urban area for destruction. While this explains why Hiroshima and Nagasaki were ultimately the targets of the atomic bomb, I'd like to take a moment to address why aiming for the Imperial Palace to try and kill the Emperor and the Supreme War Council would have been counterproductive to US war aims.

In 1945, the US did face a serious problem. By all accounts the Japanese had been defeated. The Imperial Japanese Navy and most of the Japanese merchant marine either at the bottom of the sea or hiding in harbor, immobilised due to either mines or fuel shortages. Allied aircraft dominated the skies above and the shipping lanes to Japan. However, despite all this, even if the Japanese Home Islands were taken, there was a serious problem: there were substantial numbers of Japanese soldiers still deployed outside of the Home Islands. The island hopping campaign through the Pacific had left several island garrisons isolated, but still present. Meanwhile, even with the destruction of the Kwantung Army by the Soviet offensive in August 1945, there were large Japanese armies still present in continental Asia. Allied leaders were very concerned with how these field forces would obey an order from Tokyo to surrender (and indeed, when called upon to do so, several commanders in the field balked at the idea). Allied leadership was in turn quite keen on the idea of using the Emperor to compel surrender, as the Emperor would be the only authority that might be obeyed. Furthermore, the idea of maintaining the Emperor in the post-war period to help manage the transition of Japan into a democratic state was also a matter of policy. To that end, a decapitation strike on Tokyo that killed the Emperor and other Japanese leadership had the potential of extending the war greatly, as now all the isolated Japanese forces would have to be cleared out one by one. This process would undoubtedly lead to far more casualties for all Allied forces, and could also have impeded post-war plans for Japan.

Suffice it to say, aiming to kill Japanese leadership would not have necessarily been more effective with the goal of getting Japan to surrender.