Most of the theater related databases available through the New York Public Library are only accessible at one of the research branches in the system. You can locate the research libraries (mostly at the Performing Arts Library) at: http://www.nypl.org/locations
Some NYPL film & theater databases of note:
International Bibliography of Theatre and Dance with Full Text
International Bibliography of Theatre & Dance with Full Text contains all of the content available in International Bibliography of Theatre & Dance as well as full text for 100 titles, including Canadian Theatre Review, Dance Chronicle, Dance Teacher, Modern Drama, PAJ: A Journal of Performance and Art, Research in Dance Education, Research in Drama Education, Studies in Theatre and Performance, TDR: The Drama Review, Theater, and many more. Additional full text available includes more than 50 books & monographs.
International Index for the Performing Arts Full Text (IIPA)
IIPA covers the subjects of dance, film, television, drama, recorded sound,theater, stagecraft, musical theater, broadcast arts, circus performance, comedy, storytelling, opera, pantomime, puppetry, magic and more. Contains over 172,013 records providing current and retrospective coverage, with citations dating back to 1864.