Japan's image of quality cheese has remained firmly attached to fine European imports. Processed sliced cheeses of the Kraft variety are ubiquitous, but for the "real" stuff you'd be smart to visit an international supermarket for a decent selection.
Imported cheese is certainly gaining in popularity — it's not only sold in department store basements but also specialty shops across Tokyo. There are the mainstay import-food stores such as Kaldi or Fermier, which, in addition to having several locations around Tokyo, offers online ordering (www.fermier.co.jp).
Even in regular local supermarkets, the cheese sections seem to be expanding beyond the standard mozzarella and cheddar to offer blue and cream cheeses from France and Switzerland.