The final modifier should not affect where a variable is stored. So regardless, a local variable will still be on the stack. However, keep in mind that when you reference a final local variable from an anonymous class, a copy of the value will be stored in an "invisible" variable in the instances of that anonymous class.
The mind is a strange and wonderful thing. I'm not sure that it will ever be able to figure itself out, everything else, maybe. From the atom to the universe, everything, except itself.