The building is the landmark Colony Club, designed by Stanford White. the Academy also has a school in Hollywood, on the site of the old Charlie Chaplin Studios.
There is an impressive list of alums in the Wikipedia article-- includes Robert Redford, Grace Kelly, Diana Barrymore, John Cassavetes and all kinds of names you have heard of or maybe not. It doesn't say whether these people graduated with any kind of degree, only that they attended the place.
I knew the building was the old Colony Club but it wasn't until very recently that I learned it was also this Drama Academy.
New York has all sorts of places to study acting, notably the Tisch School of the Arts at NYU ( where my friend Cecil Mackinnon teaches). I wonder how well graduates of these places do on the whole...guess it's still true that it is such a competitive profession that there is still " a broken heart for every light on Broadway."
The American Academy of Dramatic Arts is celebrating its 125th year of operation in 2009.