What would be the alternative to dropping these two bombs? Since the Japanese were nowhere near to surrender, would that be an invasion? Invasion, that would cost thousands of hundreds lives on both sides?
I've frequently heard "invasion wouldn't be nessesery, because the U.S. already controlled the air and bombings would make the Japanese quit at some point". Fair point, but it would take burning more and more cities (LeMay was very good at it), so it might have been far more deadly than two atomic bombs.
I'm not sure about drooping it on less populated area or demonstrating it on non-populated target. After all, it took two bombs to make Tokyo call it quits. I think Truman made a horrific, but right call.
Are you sure about the second bomb? Japan was given only three days to respond to Hiroshima before the Nagasaki bomb ended 40,000 more lives. After Nagasaki, we did give Japan five more days, after which they did surrender.
I voted for option 3 myself, although I would choose option 1 before 2. The bombs did save far more lives ultimately, but I do question whether or not the one-two-punch was necessary for two big cities. It depends on whether or not the quick use of the second bomb was absolutely necessary to send the message to Japan.
I do believe that something had to be done to prevent a ground invasion. I'm fine with using math as a method to reduce potential casualties. Still, care should be taken with regards to civilian life.