I don't have time to do the research but there is very good reason to believe that the USA would not have dropped the atom bomb on a European city. Call it a racist motive if you will.
As for "repeat as necessary," the USA postured that they could have bombed every Japanese city to rubble but the fact is we did not have enough fissile material for a fourth bomb. Extracting U-238 was still a slow and imperfect process; ditto with Pu-239. If I recall correctly the absolute dearth of fissile material in 1945 was a classified secret for many years.
The fact that we were still, seriously, preparing for the invasion of the island of Honshu is proof positive that Truman and the Department of War did not think that two atom bombs would not be enough to deter the Japanese.
World War II was total war! We sure as hell would have dropped atomics on Germany.
The preparations for the invasion of Honshu were because at that time we did not know if the bombs would work. We had tested one U235 bomb at White Sands, New Mexico. Therefore, we knew the one we dropped on Hiroshima would work. As mentioned U235 was in critically short supply. The production pipeline for coming bombs was mostly plutonium. The first test of a Plutonium bomb was when we dropped it on Nagasaki. It worked, its yield was actually greater than the predictions. We then knew we could start turning out workable atomic weapons on a large scale.
An irony of history is the work of German and East European Jewish Scientists. They fled to the United States because of persecution and worse by Hitler. Those German Jews were loyal German citizens. In effect Hitler gave us the bomb by driving out these brilliant scientists. They would have built the bomb for Hitler as loyal Germans if Hitler had not persecuted them.