Interviewing someone associated with a theatre or organization can be very useful for primary source research, but it's important to prepare. The Purdue Online Writing Lab has a helpful page on how to prep for and conduct an interview. Research already existing interviews with this person, so you don't repeat questions that are easily found - you want to be cognizant of their time.
Use this to search within a website. You can limit to a particular website or domain in the "site or domain" field. For example, try the word "grant" along with the name of the organization to see if they received money from a grant.
From the Internet Archive, the Wayback Machine is a digital archive of the internet, consisting of browsable snapshots of over 240 billion URLs. This is an ideal way to find historical production information about a company or group. Use the "Save Page Now" feature to capture a website as it appears now for use as a trusted citation in the future.
The NYPL Catalog searches the circulating and non-circulating research collections at the New York Public Library's Library for the Performing Arts at the Lincoln Center, including those at the Billy Rose Theatre Division and the Theatre on Film and Tape Archive (TOFT). The TOFT has many archival videos of New York theatre productions that can be viewed at the Library for the Performing Arts by researchers with an appointment.
The Broadway League has information both on attendance and on grosses, in addition to touring data and research reports.
Broadway World shows box office grosses by theatre, show, cumulative, year, and week. Grosses can also be exported to Microsoft Excel.
Playbill also has a section on Broadway grosses.
Foundation Center 990 Finder provides an access point to look up publicly stored tax records of non-profits, especially useful for seeing more detailed information on the finances of a theater or theater organization. You can normally see the past three years of an organization's taxes. Keep in mind the most recent tax information will probably be from 2014.
You won't need all of the information on a 990, you'll mostly be looking at revenue, expenses, employees, gifts and grants, programs, board members, and so on.These two pages have useful information on decoding the 990 forms.