"Finney" begins with the murder of the patriarch of a criminal family, Patrick "Tucker" Finney. Who killed him? There are plenty of suspects - from his compulsive gambler and drug addict son Tom to rival "businessman" Bobo Simpson.
Tucker's eldest son, Steven (or Finney, as everyone calls him) couldn't care less. As a sick joke, his father has left him a derelict cinema in the middle of Simpson territory. Finney decides to turn it into a jazz club, and finally pull his life together.
Meanwhile, his older sister Lena, who has inherited both Tucker's shady empire and his hard personality, has decided to find out who murdered her father...