A demonstration was indeed considered but was decided against for two main reasons.

Firstly, the US armed forces needed to gather information on the use of nuclear weapons against real urban targets, in the field. This was one factor in deciding not to use the first bomb against Tokyo. The Japanese capital had been damaged previously by fire-bombing campaigns, which meant that assessing the true combat effectiveness of the weapon would be harder. The same is obviously true when deploying the bomb against a rural or ocean target. Hiroshima, largely untouched by war's air campaigns, therefore represented a valuable opportunity for both intelligence gathering and propaganda (the Soviet Union would also see the devastation wrought).

The second identified target, Kokura, was actually ultimately spared because smoke and clouds were obscuring the city on the day of its intended bombing. While these conditions would obviously impair the attack, it was also vital that US reconnaissance planes could subsequently photograph and document the destruction, both for their own studies and for impact on the world stage. Two planes dedicated to measuring and documenting the blasts accompanied both atomic bombing missions in Japan.

Secondly, the lack of viable replacement weapons made a demonstration exercise excessively risky. Since 1945 we have seen a thousand nuclear and thermonuclear detonations, but during WW2 stockpiles of this size simply did not exist. Any number of factors could cause an operational failure during a demonstration, which would still expend a bomb not easily replaced. For example, such new technology made a mis-firing not unlikely, which in turn would lack the desired psychological impact on the Japanese. The risk of intervention from the Japanese armed forces was also considerable, especially if prior warning of a demonstration was given.

Any delay caused by replacing a bomb or rescheduling a demonstration was therefore likely to be strategically disadvantageous to the United States. Of course there was no guarantee that a demonstration would even work, as Japan did not surrender after the bombing of Hiroshima. The loss of life predicted in a ground invasion of Japan was astronomical, which put significant additional pressure on the nuclear strategy. Further to this, the anti-war sentiment which the US was attempting to incite within Japan (variously with fire-bombing and pamphlet drops) would be far better served by hitting a real, hard target, rather than a hypothetical one.

Edit: Typing.