There are an increasing number of public poker games in Tokyo. Gambling is illegal in Japan, however, so public poker games cannot be for money. Instead, most games are for points that can be collected for prizes, or for credit coupons at the pub holding the game.
These games are run by Japanese groups, and are attended mostly by Japanese players (with the occasional foreigner). Foreigners who would like to participate should be prepared for mostly Japanese language when joining and playing the games, although most Japanese will try to accomodate an English speaker as best they can according to their own English abilities.
There are probably a number of regular home games played in the English-speaking community in Tokyo. Unfortunately I don't have any information to pass on about those games.
There are two main groups in Tokyo (that I know of) that host poker games open to the public. The first is the Japan Poker Player's Association, currently based at a dedicated card room near the Ueno district of Tokyo. The second is the Japan Poker Enterprise Association, a group of pubs and restaurants that hold tournaments in a common league.
A new group called the Japan Poker League has also started holding tournaments in bars and clubs across Tokyo.
Click here for the entry on the Japan Poker Player's Association.
Click here for the entry on the Japan Poker Enterprise Association.
Click here for the entry on the Japan Poker League.