Unfortunately the institutional rate for online subscriptions to the New York Times through their website is prohibitively expensive. We do have access to the text of articles through Nexis Uni (formerly LexisNexis). You can search for a specific topic or article, but not easily browse. (You can also click on the Journals link on the library homepage and then search for New York Times).
We have a paper copy of the NYT for the most recent week on the 1st floor of SFL.