I sew quite a bit and here are a two web sites with wonderful Japanese fabrics:
The International Fabric Collection has a good reputation as a source for beautiful traditional patterns. They have quite a good selection of Chirimen cotton and rayon, Yukata, Itaya and a whole lot more:
Report Depot has a more modern selection of Japanese fabrics, all are funny, campy and just beautifully printed:
As Bronwyn points out one US "Fat Quarter" is enough for a furoshiki.