Of all the Japanese cities, Tokyo is perhaps the best place for shopping- it’s got loads of variety, because nearly everything produced in Japan- from electronics to handicrafts- eventually finds its way to the capital. There’s an entire array of depatos (department stores), shops, and markets including the amazing Tsukiji area: the largest fish and seafood market in the world, and there’s little you won’t be able to find in Tokyo. Among the well-known shopping districts of Tokyo are Ginza with lots of boutiques and depatos, Akihabara for electronics, Asakusa for souvenirs and handicrafts and Omotesando, with its antique shops.
You should try to buy handicrafts and traditional arts in Tokyo- they’ll be comparatively cheap, authentic and the type you won’t find outside the country. Look, especially, for ceramics, textiles (kimonos too), Japanese dolls, and lacquerware.