Found it!

 This is a typical street in this area. It is very short so the area is a maze and it is lined with private homes. I did not see any businesses or companies as I wandered around looking for the Shrine. The problem was that this area is not well defined in my little map book that I carry when walking. Only a couple of the main through roads are shown and the shrines are not marked.

 I finally located it. This little building contains a Buddhist altar and the sign on the lintel says that this is number 80 of the 88 sites on the Nakagawa 88 Places, obviously copying the Ohenro Pilgrimage's 88 temples in Shikoku. Since visiting I have been trying to find out more about this but so far have been unable to find more than a single website on which the Japanese will not show properly.

Moving closer to the above building and turning to my left, I found a torii with a sign identifying a Shinto shrine on the same property. I am not sure about the pronunciation of the name, but it is probably Ama Jinja, Heaven Shrine in English. This area has lots of nonstandard pronunciations. For example, the area that I live in is called Nakabaru, which would be Nakabara in standard Japanese.