First of all, big welcome to Tomcatboy48237 and wwj6392. I'm glad you decided to join!
Good point Tomcat. Although I don't believe much in the Self Defense force thing much (Japan deployed troops to Iraq) I think you have a fair point, that Japan operating F-22s has more pros than cons for the US. Also if Japan operates them, and the US operates them from Japan (and South Korea probably), it makes it worthwhile to put infrastructure and logistics into place for premanent deployment. However up till now, the US wants to base them at Alaska (Elmendorf AFB) and Hawaii (Hickam AFB) I think, both already pretty close to east Asia. So not exclusively to the West as you said...
The others up till now are currently Langley AFB and preferred is Holloman AFB.
Japan is also one of the few allies with enough budget to acquire them, and one of the few allies that would want it without destabilizing the region.
The only problem with such a sale to Japan, I think, is that Taiwan will be requesting them next. China (probably one of the biggest trade partners of the USA) won't be happy about that you know.