In addition to freebies and prizes, the day will include performances by Joe Iconis & Family, TADA! Theater, and more.
The new comedy reenacts four recent preposterous sex scandals.
The Tom Stoppard revival also features Maggie Gyllenhaal and Cynthia Nixon.
The Tony winner will step into the role originated by Jane Carr.
The 12-year-old Broadway veteran will reprise the role he played in the choral piece's San Francisco premiere.
Patricia Clarkson and Alessandro Nivola also star in the drama.
Shut Up When You Talk to Me will be presented as part of MCC Theater's Playlab series.
The Southern Gothic thriller will be presented by the York Theatre Company.
The Vineyard Theatre production is directed by television legend Garry Marshall.
Wicked's Christine Dwyer, The Last Ship's Eric Anderson, and more will star.