Takashi Miike does a lot of yakuza themed movies. (he's my favorite director!)
My personal favorite is Ichi the Killer, but it's kind of gorey so if you dont have a strong stomach do not watch it.
But otherwise maybe his Dead or Alive Trilogy should a be good choice! He also made the live action of the game Yakuza (in japanese it's called "Ryu ga gotoku")
Just to warn you, Takashi miike is kind of obscure and does a lot of random sh*t in his movies. But i think you should be alright with Dead or Alive
Dead or Alive: Hanzaisha (1999)
(Read the Warning!)
Ryu ga gotoku (Like a Dragon, Yakuza)
Ryû ga gotoku: gekijô-ban (2007)