Honestly, if the point was psychological, the Amero's could have nuked a purely military area, or even an empty field of some kind. Didn't HAVE to nuke a city.
Might not have had the same emotional effect, but if it went "field" and then "military base" along with wording to the effect "We'll keep ramping up until you surrender," I doubt it'd have taken much more...
They had very few bombs at the time...
The Japanese didn't know that.
Note: I am not in any way endorsing the morality of the actions of the Americans. I am a pacifist, although, as MSH said earlier, I'm not sure how that philosophy would stand up under fire.
From what I remember, the main reason the nuclear strikes even worked in the first place was because the Japanese didn't think a single plane could do that much damage. If they'd had the knowledge of the capabilities of nuclear weapons before they were used on a major target, they could have taken preventive measures and negated the American ace in the hole. Tactically, it made sense. Morally, it was reprehensible.
EDIT: Wait, what does this have to do with abusive policing? I suppose I'll have to say something about that if I want to avoid participating in a derail:
Who watches the watchers? In [Some/Most/Whatever parts of]America[And elsewhere], the answer is "No one. Or at least, no one with power enough to do anything about police misconduct or enough morality to use that power.".