The United States did target military and civilian institutions in Japan; the atomic bombings were an extension of a conventional bombing campaign that included dropping napalm on 67 Japanese cities before the first atomic bomb was dropped on Hiroshima. For more on this, you may want to consult the following threads from our FAQ:

• Did the US have to nuke Japan in WWII?

• Why weren't the bombings of Hiroshima and Nagasaki considered war crimes? The United States wiped out hundreds of thousands of Japanese civilians. Was this seen as permissable at the time under the circumstances?

• Did the atomic bombings in Japan indirectly prevent the deaths of more Japanese citizens than they killed?

• TIL that Kokura, Japan was the original target for the 2nd Nuclear Bomb in Japan. However, it was too cloudy to drop it on Kokura and Nagasaki was a secondary target. Why did the Allies believe Kokura was a more valuable military target than Nagasaki?