Around here we mainly look at the exclusives or versions which maybe did not make it out of Japan entirely intact, possibly with an eye to ones you can play with no/minimal Japanese knowledge. Not sure what I want to suggest if you are in Japan and buying Japanese games as a general concept.
Minna no soft tetris/Tetris Advance Japanese version is the best commercial tetris game on the GBA. Homebrew wise it is pretty much Tetnus on Drugs/Lockjaw that beats it.
There are a whole mess of puzzle games that were Japan only. The sequels to Kuru Kuru Kururin being among the more notable for me.
Super Robot Taisen eventually made it outside Japan in some form, however if you can speak Japanese I would suggest those.
Also if you can speak Japanese the medabots/medarot RPG sequels/remakes were good stuff.
Haro no Puyo Puyo was a nice little gundam themed puyo puyo title.
As ever Japan put a Lode Runner version where elsewhere did not.
The bomberman games which never made it out of Japan can be worth a look, however you are not going to miss much if you don't really care for story bomberman.
