Ok, some of this info is a few years old, and I don’t know Japanese, but here is what I found:
At the Department Store Tokkyu Hands in Shinjuku (located right outside the station, next to Kinokuniya) you may find traditional Japanese games and modern games.
There’s a game publisher that owns a shop to sell games. They are locate near the Tokyo Dome.
5F Umezawa Building
1-1-15 Kouraku Bunkyou-Ku
Yellow Submarine is a small chain with a few locations, notably in Akihabara and Shinjuku. They seem to specialize in RPGs (like Dungeons and Dragons), Miniatures (like Warhammer) & CCGs (like Magic the Gathering), but have other types of games too.
Here are maps to their locations:
Akihabara should have several places to find games. A couple that I found besides the Yellow Submarine:
Shosen Book Mart: This is supposed to have a great selection, but apparently to get to the game section you have to venture through the porno section, so enter at own risk!
Yodobashi Camera Akihabara: should find games like monopoly, life chess and go here.
If you are looking to meet other gamers, Japan`s International Gamers Guild meets about once a month. They describe themselves as “Japan’s largest and longest running English speaking and bilingual gaming group.” Show up and they may better suggestions, and you may meet some new friends to play games with.
And finally, Here is a map showing game shops around Tokyo:
Board Game Geek: