If we had not had atomic weapons, we would have invaded the Home Islands. It would have been like Okinawa, but worse. Our boys would have had to kill just about everybody to secure those islands.
Leave aside, for a moment, the American losses, which would have been huge. The loss of life on the Japanese side would have been in the Tens of Millions.
Those atomic bombs were the best thing that ever happened to Japan, because of what they prevented. It is an ugly truth, but war is an ugly business.
Not to mention the likelihood of calling in the Soviets to help and ultimately partitioning the country as with Germany and Korea.