The question of making a "demonstration" before using the bomb on cities was explicitly considered. A team of scientists at the University of Chicago explicitly advocated it in the so-called Franck Report, a petition went around Los Alamos calling for it, and it was eventually considered at a very high level by the top scientists on the project. The scientists concluded that "we can propose no technical demonstration likely to bring an end to the war; we see no acceptable alternative to direct military use." The military figures were also afraid that the bomb might be a dud and thus wasted.

As for why not an isolated military site, you misunderstand the point of the bomb. It was meant to be a spectacle, something un-ignorable, something that might break through the stalemate with regards to the Japanese high command. From the perspective of the scientific and military advisors, the ideal target was Kyoto, which had no military installation whatsoever, because it was "an intellectual center for Japan and the people there are more apt to appreciate the significance of such a weapon as the gadget."

Kyoto got nixed from the list because Secretary of War Stimson thought that destroying a purely cultural center would be unforgivable and wanted the first use to be on a target that contained a military justification. Specifically they wanted to make sure 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." That is, it had to be a military target embedded in a larger city, so that the damage would be obvious even if they missed the target significantly.

The military pushed for Kyoto all the way up until the actual orders to use the bomb were issued. Stimson pushed back. He convinced Truman that Kyoto should be off the list and the first target should be "military." Stimson was under no illusions that these "military" targets, like Hiroshima, were also full of civilians, but somehow Truman came away with the idea that they were going "to use it so that military objectives and soldiers and sailors are the target and not women and children." Which obviously was incorrect and should have been obviously so — I think Truman was being rather stupid about this, personally. (Truman was incurious and out of his league when it came to the bomb, and he has many instances of this kind of confusion.)

To get to your last question, did the US really care about the civilians? Of course not. They cared about winning the war at almost any cost (to the enemy). They designed their firebombs specifically to destroy civilian housing and had been ruinously dropping napalm bombs on paper-and-wood Japanese cities for months before the atomic bombs. All sides in World War II practiced a stance of total war, targeting civilians when they thought it would be expedient to their military goals. In the case of the US targeting Japanese civilians, they argued that the dispersed nature of Japanese industry meant that to bomb industry you had to bomb civilians. One does not have to accept that as an ethically rigorous argument, but it is important to understand the reasoning well before critiquing it.

If you read some of the key books about the A-Bomb (The Richard Rhodes one for example) there was intense discussion about this at the corridors of power in the US. There was discussion of dropping on an uninhabited island, allowing time to evacuate, etc. In the end the decision to bomb cities was based on the idea that it was the strongest message. Given that even after 2 bombings it required an unprecedented direct message from the emperor (there was huge resistance to this as well, and many attempts were made to stop this from being broadcast. by right wingers in Japan) to force the end, even that was barely enough. Given the Japanese plans to use every available man/woman/child in human wave assaults and the experience of the mass suicides in Okinawa the decision to drop the bomb likely saved several million Japanese civilians. Possibly even from a extermination level event. Once the "cat was out of the bag" about the bomb it quickly led to the public and officialdom begining the long process of re-thinking war it self. The idea that was was not longer the death of the "little people" changed the thinking of the powerful was slowly growing.

TL;DR Yes, but the decision was made so as to be more dramatic, and even that was almost not enough. It likely saved 20 Japanese lives for each one it killed. To say nothing of US casualties..

Bibliography: Too many to easily reference, and many from the Japanese. I loathe linking to Wikipedia, but I suggest it only for the list of references at the bottom of the article. Take a look, don't just trust me. Even the old Time-Life books have excellent references at the end of them.