First off, the U.S. only had 2 bombs ready. The third would not have been ready for 8-10 days after the bombing of Nagasaki. As for which hypothetical city would have been bombed, the answer is likely Kokura, which was the primary target the day Nagasaki was bombed.

However, the U.S. had a list of 5 potential targets (including both Hiroshima and Nagasaki), so any of those 3 could have been chosen based on disposition of air defenses, visibility, weather, bomber range, etc.

Source: Sherwin, Martin J. (2003). A World Destroyed: Hiroshima and its Legacies. Stanford, California: Stanford University Press.

They never made solid plans that far in advance.

Truman approved 4 targets in July 1945. These were, in order of priority, Hiroshima, Kokura, Niigata, and Nagasaki.

On August 6, Hiroshima was primary, Kokura secondary.

On August 9, Kokura was primary, Nagasaki secondary.

So that would leave Kokura (an obviously "military" target) and Niigata (a harder target to reach than the others).

On August 10th, Truman issued a "stop" order on further atomic bombing, pending his decision to bomb further. There were discussions by the Manhattan Project staff as to whether they would want to drop the next bomb as it was available, or to "save up" several bombs and then drop them simultaneously. There was an Army Air Force guy who wanted Tokyo added to the list of possible targets for the next one.

But none of those questions got vetted at the top, and since Truman had issued a stop order, any further target approval would have had to go through him personally. So there is no way to know what would have happened.

Admittedly this is speculative, as I do not believe there was any solid planning framework in place that specifically designated a third city to strike if the first two nuclear bombs did not establish a surrender scenario. I will say that I think it very possibly would have been Kyoto though.

Kyoto was actually initially in the running to be one of the first or second strike cities, because it did have military and industrial significance, and was considered an intellectual and cultural center of Japan. Prior to August of 1945 though, Kyoto was actually removed from the prospective target list. Kyoto was removed initially due to the demand of the US Secretary of War, Henry L. Stimson. The reason was because Stimson thought Kyoto was a beautiful city with too much historical significance. Stimson had even spent his honeymoon there a few decades earlier, and made it very clear he did not wish to see it destroyed. Stimson argued with General Curtis LeMay about this, and LeMay heavily disagreed and wanted Kyoto left on the list, so Stimson actually lobbied President Truman directly about this, and Truman finally agreed with him to not bomb Kyoto (or Tokyo) for the reasons Stimson gave.

Now, the reason I still say Kyoto (or perhaps Tokyo) though as the potential third target is because we have to play the game of "what if?" here. What if the devastating effects of the first two bombs at Hiroshima and Nagasaki had not proven enough to force Japanese capitulation? Had that been the case, then I have little doubt that the initial reasoning for Truman agreeing to avoid Kyoto (and Tokyo) would definitely have at least been re-evaluated and re-debated, and that prior reasoning to avoid them as target cities very well could have been changed to them becoming high priority targets. If the first two bombs did not get the Japanese to surrender, then America would have had to ramp things up even further, and the destruction of Kyoto, or the capital Tokyo, would have been the way to put the most pressure on the Japanese to surrender - more-so than hitting say, Yokohama or Niigata, which were also in the running as target cities.