There even had been discussions of doing a test off the coast of Japan but in full view of say Tokyo. Or even in a less populated area near some major city. But for a variety of reasons those ideas were decided against.
Only trouble is, none of those reasons has ever seemed very convincing to me. It's true that the Japanese didn't even surrender after losing one city, and took a while after the second. So a test might not have worked. But the US didn't know that in advance. (There's also the question of the overtures being made by elements in the Japanese hierarchy to sue for peace via back channels through Switzerland. Last time I discussed this Mathiaslg sent me a PM telling me I was wrong, so maybe I am. One thing's for sure, the Bomb got them far better terms than any other peace would have done.)
One factor may be that they only had two bombs at that point (I think). They wanted to give the impression that they had an inexhaustible supply of the things and could just cancel city after city from the earth (and that's the real power of the A-bomb - a psychological power... as others have said more damage was done in some conventional raids). But in reality if Japan had kept going it would have taken a while to get another bomb into action.
Another factor is the inherent tendency for new technologies to be used. When some of the Manhattan Project scientists - notably Szilard - set about arguing against use, they met with total incredulity from the top brass. They told him straight - I'm paraphrasing - "You understand that having spent all this time and money building this thing, we are going to use it?" They'd spent a couple of billion dollars and basically built three cities from scratch to get this toy, getting a major strategic head start on the Russians...there was basically zero chance of them just sitting on it. In fact, what's amazing is that it has never been used since. MacArthur was probably keen on using it in Korea (though he denied it), and Kennedy was under huge pressure from his generals during the Cuba crisis. I'm surprised it wasn't used in Vietnam.
But I do think the 'message to the Russians' thing played a big part. "This far and no further, Joe". In fact, people totting up the costs on both sides ought arguably to consider the costs of a war with Russia before 1950. It's especially interesting that Truman played poker for about 2 weeks solid before he made the call (or rather, raise).
That said, I don't really get Steve's point about soldiers. Soldiers at that point were ordinary citizens, and they were being killed in numbers that are inconceivable today. I think the absolute apocalypse that a land invasion would have been surely played
some part in their thinking.