Possible Clues:

• Award given by ''The Village Voice''
• Showbiz award
• Beckett award
• Certain acting award
• Award for 'The Curse of the Starving Class'
• Award for 'Six Degrees of Separation'
• 2012 honor for '4000 Miles'
• Award won by the play '4000 Miles'
• Award for 'The Zoo Story'
• Stage presentation?