Begin by Using the Articles via Databases tab which you find on the Library Page https://library.nyu.edu/ to find a good selection of databases. You will then be able to select Search for articles within databases grouped by format or subject, in this case Theatre. You can search 10 databases a time http://arch.library.nyu.edu/databases/subject/theatre .
If you would like to target just a few databases at a time, here are a few suggestions
Looking for a more in depth look at Theatre articles? Then go to my Theatre libguide. This is a selective guide to theatre literature is the gateway to books, journal articles, Primary Sources and web resources. https://guides.nyu.edu/Theatre