This is by no means an exhaustive list of places, just the ones I managed to get to.
Walnut Kyoto & Tokyo
I went to both, because, why not? But I have to say that you probably don't have to.
It's a good stop if you are a fan of Amirisu magazine because they have lots of Amirisu samples, and they're a flagship for Brooklyn Tweed and Quince & Co, I believe.
Avril Kichijoji (Tokyo)
I only went to the one in Tokyo. I decided against visiting the one in Kyoto because I did not buy anything in Tokyo. They have a lot of novelty yarn, which is so not the kind of thing I knit with.
Update: yarnoversteffi kindly gifted me the thing I most wanted from Avril in our Singapore knitters Christmas yarn swap, so that was awesome.
This is much more a shop for weavers and spinners.
They have a lot of hemp, lots of animal roving (the wool is from New Zealand though) and quite a selection of natural dyestuffs.
They do carry silk, but they were not able to tell me the yardage per 100g or anything like that, so I didn't get any. It's possible that I was unable to explain to them what I was asking, so maybe you will have better luck.
They have more rustic-type yarns than the other shops in Tokyo that I managed to get to. It was nice, but they did not have much stuff I was likely to use in the next 6-12 months. They stocked some Scottish yarns, but I am planning on attending Edinburgh Yarn Festival again, so I didn't get any of it either.
I made it here because they have coned yarn, and that's something I keep an eye out for because I do have a knitting machine. They had a good selection of finer, lightweight yarns suitable for tropical weather, including Belgian linen.
And they also had DK weight cotton cashmere, which I am very fond off.
Hobbyra Hobbyre (Kobe)
I stumbled on this one by accident.
The shop is adorable, and I picked up some of their house brand yarn, including a lovely linen blend.
This was my favorite. They carry a good mix of hand-dyed European/American yarns as well a good selection of warm weather friendly ones. They are also a Zealana stockist.
They also carry Saredo recycled yarn, which was something I had been looking for.