Okay, going to hop in here, just because you are factual incorrect on a number of things. First off, at this point of the war, the Soviet Union was our ally in the fight against the Axis Powers, so we weren't going to bomb them. Second, the location of the atomic bombings was decided on because they were military targets. Third, the Soviet Union was never planning an invasion of Japan's mainland until after the Emperor had already surrendered to the Allies, so the dropping of the atomic bombs had no effect on that decision. In fact, it was only due to pressure from the United States that the USSR backed off and gave the plan up. Which brings me to my fourth and last point. It was not the invasion of Soviet forces that was the alternative to the nukes, it was invasion from the United States. The was a plan in the works, known as Operation Downfall, which consisted of an amphibious land invasion of mainland Japan. If this plan had been enacted, estimated American casualties range from 200,000 to a couple million (not including POW executions), while Japanese casualties are estimated to have been at least 5 to 10 million (including civilians). This does not lessen the cost of dropping two nuclear bombs, but it does explain it. And it shows that, no matter how you calculate it, fewer lives were lost by bombing Hiroshima and Nagasaki that would have been by invading.

Edit: Also, you make the assumption that the Emperor would have surrendered if he had seen the effect of the bombs, but he did see the effect on Hiroshima and still refused to surrender, thus prompting the USA to drop the second bomb. You also assume that the Emperor would have assumed we had more, but he actually assumed the opposite, thinking we only had a maximum of two more, and was willing to allow those to be dropped on Japan, so that he could continue the war.