SirPupNYC you are correct about the Vivian Beaumont - as well as the Mitzi Newhouse. Both are designated as 'theaters' by LCT, which is also, Lincoln Center Theater. Although every other site I have found calls them 'theatres'.
The Public is a 'theater' and all of their venues are 'theaters'. It's Second Stage Theater.
But it's The Manhattan Theatre Club; The Signature Theatre (Linney Theatre, Diamond Theatre , etc); The Vineyard Theatre; Roundabout Theatre with American Airlines Theatre, Stephen Sondheim Theatre etc;
My favorite is Jujamcyn Theaters - resolutely using the American spelling. But all of their venues use the other spelling - Neil Simon Theatre, St James Theatre, Walter Kerr Theatre etc |