Ito-ya has many shops, but when I need paper of any type for a project, the Ginza branch is where I head. The clerks "know their stuff" and are very helpful. Large orders were accurately shipped. I'll also go here for small presents for people back home, to get "real" instead of "tourist" stuff.
Ito-ya 3 is simply incredible. It's full of traditional Japanese papers, and it caters to Japanese calligraphers. If you don't know anything about Japanese papers, then you're going yourself a disservice. Jun'ichiro Tanizaki wrote about the pleasantness of Japanese paper. It captures light, and its textures are sublimely sensual. As you might expect, because of Japan's proximity to China, Japan has a long history of paper making. Mulberry paper and washi paper are particularly famous. Ito-ya 3 has a large selection of both. You can also buy traditional bound blank note books. If you're looking for a calligraphy brush, stones or ink, you're in luck. They seem to have every imaginable type from the traditional to the modern. On the lower floors there various traditional Japanese accouterments, like book covers and large handkerchiefs. Even if you're not a calligrapher, go and take a look. You won't regret it.