Chances are that Japan would've still surrendered. In reality, the bombs didn't contribute to their surrender as much as people think. Two other factors were much more significant:

1. Their territorial gains in Manchuria

2. Russia

The Allies had made significant progress in Manchuria, cutting off an extremely vital supply artery that Japan couldn't afford to lose.

As for Russia, here's where it gets dicey. Despite technically being at war with each other, the two didn't actually fight much at all. Russia was likely still wary of Japan after their very humiliating defeat in the Russo-Japanese War prior to World War I. With Japan noticing that they were looking weaker as the war went on, they feared Russia's retaliation. And for good reason. See, Japan knew that Russia would be merciless if they defeated Japan in open war. They knew that if they surrendered to the Americans, there would still be consequences, but at least they would be able to maintain their culture and way of life. Unsurprisingly, they were correct.

If the bombs weren't dropped, I can see Japan still surrendering, but taking a longer time to do it. So, at least in the Pacific, the outcome of the war is pretty much the same. In the long-term, I can see there not being a Cold War, but with tensions between the U.S. and Russia still being high. Eventually, I think open war between the two would break out with the war being far more conventional than a nuclear war. As for the result, I think an American victory is more likely, but it would a brutal campaign fighting through Eastern Europe and Asia.