I spent a couple of weeks in Japan back in the early '90s, and didn't encounter any cultural issues when photographing. I'd be surprised if you encountered "staring at the gaijin", as I think most Japanese are too polite for that. I had the same experience while in Taiwan, although I did encounter a bus-load of young school girls who ran up and wanted to practice their English, and take pictures with the bearded American.
In Japan, I ran into only a couple of areas where photography was prohibited, and this was clearly posted with multi-lingual signage. I have no idea about tripod restrictions, though. On several occasions I also encountered English-speaking locals who were part of a large group who try to assist tourists as they go about their daily routines. Apparently, I looked confused when trying to figure out which subway to take, so they'd come up and, speaking in English, ask if they could help. I'm not sure if that practice still exists, or will be available in the city you'll be visiting, but I thought it was great.