To determine in what issue of the New York Times your play was reviewed:
Once you've determined where the review appeared, you need to find the specific roll of microfilm for the New York Times for that issue of the newspaper. Microfilm for the New York Times is on the main floor, near the reference collection.
The New York Times is available in full text through Nexis Uni (1980-current). When you open the database, the News search should be highlighted in blue. If not, click on it. This is what you will see:
In the “Search in all News” box, type: term(theater reviews) AND [name of the play, in quotation marks]
For example:
You can use the "Choose date range" menu to search a specific range of dates. Then click "Search."
To the left of the results, click “Sources” to select reviews from a specific publication:
Other facets to the left of the results let you limit by Location (state or country), People, etc. Or you can "Search Within Results" for a name or keywords.
You can also search back issues of the New York Times at its website (though you may not get free access to the full text of the review):
https://query.nytimes.com/search/sitesearch/
To the left of the search you can limit to a specific date range. Use quotation marks around the title of your play.
Each article found on the New York Times website can be found in Nexis Uni. The newspaper's website search results emphasize the headline used online, but each result also includes its print headline, which is used by databases such as Nexis Uni. For example, a search result on the website:
Copy the Print Headline and search for it (in quotation marks) in Nexis Uni:
Here is the Nexis Uni search result: