[Lonthego]

You just can't beat Kyoto when it comes to Shrines..

Have you been to Kamakura yet?? In Kanagawa prefecture, transfer at Yokohama. I'd be surprised if you haven't since you mentioned the bit about already having been to tourist heavy areas, but man I love Kamakura. Granted it leans mostly towards temples, but there are some great shrines too..like the one with the tengu statues on the side of a mountain (Kousokuji??).

Also, if you are around the area, in Kichijouji (about 15-20 mins from Shinjuku station) there is a very pretty shrine on the water in Inokashira Park, though the park itself will be crowded because it is a popular and beautiful spot to spend the afternoon or weekend. Grab lunch in town and go check it out.