This trip, I stayed in Sapporo, Zao Onsen, Sendai, and a few nights in Tokyo.
Outside of the adult entertainment industry, and a store that sold weapons inter alia, I didn't face any discrimination on the basis of race or nationality. I went to bars in all of these locations, and didn't have any problems. I went to onsen in Zao Onsen, Tsuru no yu onsen, and Odaiba onsen, and far from banning foreigners, all three provided English-language information of one sort or another, and the latter two also had Korean-language info.
I had mixed success with hostess bars. I tried a couple of hostess bars in Sapporo with no luck, and all but one of the touts I came across ignored me. However, in Sendai, one place touted itself to me and I spent an hour there.
Somewhat frustratingly, even though I wasn't allowed in hostess bars in Sapporo, I came across touts for スペシャルマッサージ (Supesharu massāji) in both Sapporo and Sendai. As far as I remember, they almost always spoke in English to me! When I explained that I was looking for hostess bars, not massāji, one tout helpfully explained that that wasn't possible in Sapporo, but that as well as massage parlours, he had a soapland that I could go to. Kekko desu (no thanks)!
I only saw one "no foreigners" sign in Japan. It was outside a soapland in Sendai.
So in conclusion, rural versus urbanized didn't make much of a difference in this trip, nor did my specific nationality help much, and it wasn't much of a problem outside of the adult entertainment industry.