Why did the Japanese government choose to have two cities destroyed by atom bombs instead of just one?

Answers above stressing the importance of honor for japaneses are accurate. Along with that, the japanese leadership believed after the first bomb that it was a conventional bomb of gigantic proportion, thus that it was sustainable. Japan had been informed of the existence of the bomb and was offered to surrender. They were offered a second time after the first bomb. They finally surrendered after the third warning.