The best stage directors are people whose work rarely (if ever) appears on Broadway-- people like:
Elizabeth LeCompte (of The Wooster Group)
Richard Foreman (of Ontological Hysteric Theatre)
Ariane Mnouchkine (of Theatre du Soliel)
Robert Wilson (whose work often appears at BAM)
Julie Taymor (whose productions at Theatre for a New Audience (before she hit it big with the Lion King) were stunning)
of the current "Broadway" directors, I admire George C. Wolfe and Jack O'Brien for their versatility.
"Inside every actor there is a Tiger, a Pig, an Ass, and a Nightingale. You never know which one is going to show up."
-John Michael Higgins in FOR YOUR CONSIDERATION