You can read the minutes of the Target Committee meetings to learn about how they thought about targets. Specifically, they were looking for targets that were:

(1) they be important targets in a large urban area of more than three miles in diameter, (2) they be capable of being damaged effectively by a blast, and (3) they are unlikely to be attacked by next August

On their justification for various targets, they saw the attack as mainly psychological:

A. It was agreed that psychological factors in the target selection were of great importance. Two aspects of this are (1) obtaining the greatest psychological effect against Japan and (2) making the initial use sufficiently spectacular for the importance of the weapon to be internationally recognized when publicity on it is released.

B. In this respect Kyoto has the advantage of the people being more highly intelligent and hence better able to appreciate the significance of the weapon. Hiroshima has the advantage of being such a size and with possible focussing from nearby mountains that a large fraction of the city may be destroyed. The Emperor's palace in Tokyo has a greater fame than any other target but is of least strategic value.

And they explicitly decided not to use it on a purely military (less collateral damage) target:

A. It was agreed that for the initial use of the weapon any small and strictly military objective should be located in a much larger area subject to blast damage in order to avoid undue risks of the weapon being lost due to bad placing of the bomb.

So you can see an interesting mix of motivations here. The goal was to destroy cities because they (the scientists and military men at the meeting) thought that would have the most profound psychological. They also worried about the accuracy of the weapon, and so trying to destroy anything that wasn't embedded in a large urban area was seen as psychologically dangerous (it might cause the bomb to be perceived as nothing new).

It is of note that Kyoto was their primary desired target; this was overruled by the Secretary of War, and so Hiroshima became their new primary target. Nagasaki was only added to the target list at the last minute, to replace Kyoto, and was not the primary target for the second mission (that was Kokura, but there were clouds). For a number of reasons, Nagasaki was a much lower-priority and less-ideal target that Hiroshima, Kyoto, or Kokura. (Niigata was on the list, but not really capable of being bombed in the first missions; once Kyoto was removed — it was too far away from the other targets to have or be a backup target.) The Nagasaki mission, as an aside, suffered from a great many mishaps that were largely covered up (the Hiroshima mission was by contrast an unambiguous "success" from the perspective of the planners).

The goal was to impress upon Japan, and the world, the psychological power of the atomic bomb. The hope of the military was that this might end the war with Japan faster. The hope of many of the scientists and policy people (like the Secretary of War) was that it might accomplish that and might impress upon the world that nuclear weapons were something "revolutionary" in the world, and needed international attention. (They knew that the future would involve more weapons and larger ones, and felt that the best long-term plan for the world was to make the first use of the weapons as horrid as possible.)

So yes, they could have targeted other kinds of facilities. They explicitly chose not to, because they had different ideas of what the purpose of the weapon would be. It should just be also noted that there have been many different views (and still are) on the optimal "utility" of nuclear weapons — your view (that nukes are good for counterforce and command and control attacks) was not actually US policy until the 1960s or so, and even then has gone different directions (and is not shared by all nations). It has its downsides (targeting counterforce requires MUCH larger arsenals for deterrence than targeting cities, and if you target command and control facilities you are guaranteeing there is no way to "terminate" the war short of total destruction).