Goldendalton, your post reminded me of my thoughts, and what I have dealt with over the years here.
I live in the relative countryside and have been dealing with this for years. I still find it strange that people will stare at you as you walk towards them, but if you acknowledge them with a Konnichiwa they tend to get embarrassed and ignore you. As others have pointed out, it rarely if ever happens in Tokyo and I feel so comfortable there. But if you just go 90 minutes out of Tokyo, it is a whole different world where tall non-Japanese men are objects of interest. It isn`t you that is imagining this, it really is happening. You really are being stared at. Not all the time, but often enough. Sometimes the interest is intense.
If you have lived in Tokyo or another major city your whole time in Japan, you may not understand what I am talking about.
I usually just ignore the stares. Every so often I try to make it more friendly by nodding, but often my friendliness is met with a blank stare or a quick look away from me. Sometimes I wait for them to bow then I say konnichiwa. Actually saying Konnichiwa
first is usually too much for them. A bow sometimes works then they say konnichiwa. That`s worked the best for me. The police too, will stare at you out here. That used to really annoy me, a guy with a gun, staring me down. (Don`t they know me by now, I have lived here for years?!) Now though I look right at them, give a small bow and a loud Ohayo Gozaimasu or Konnichiwa and they respond in kind. I am over 200 pounds and 6` 1" so to them I am a giant, even to a policeman who has a gun but is only 5` 8".
The Japanese women can be fascinated by us, or intimidated by us. We are BIG to them. We move differently. Our hair colour is different.
This also leads to chances with women. So I try to take the good with the bad, and find the staring and other issues only really bother me when I am tired. I use it as an indication, I need to have a beer or a nap or get laid! Hope this helps! Just my two yens worth.