Two points about the military thing.
First, you're probably aware that the US military has been cracking down hard on guys who start fights when out on leave. A single incident can now lead to dishonorable discharge. As a result I believe there is far less behaving badly in Roppongi than there used to be, and consequently you should run into less friction as a result of being US military. See how karma works?
Second, you're also probably aware that your unit does NOT want you to "flaunt the military thing." Keep a low profile. The days when GIs hung out in their fatigues on city streets smoking are long gone.