Without the nuclear bomb, Japan's prospects are bleak.
I know many think wow how can you say that they lost two cities. It would have been much worse had the Allies had to invade the mainland.
You would probably be looking at the use of biological/chemical weapons to soften up the Japanese mainland, followed or in concert with an immense bombing campaign similar to what destroyed much of Europe. By the time the troops actually landed you'd probably have millions of casualties in Japan, virtually no infrastructure, navy or air force remaining. Disease and famine would be rampant. Probably less than 10% of the Japanese people survive the fall out of such an event. This would butterfly of course into all kinds of potential changes. The war would of dragged on for another 3-5 years at least. With perhaps pockets of resistance surviving for a decade or two in the former Japanese Empire.
Few people on this board would argue that Operation Olympic was the better alternative to the atomic bombs on Japan. It's more or less agreed that while it wasn't a nice option, it was "the better" one.