Subscribe to Backstage. The show business magazine has an online component with job listings and audition listings. The auditions are national, but can be narrowed to just New York. Backstage has several levels of subscriptions, including a Backstage East listing service and access to their online magazine.
Check the Backstage blog, which is affiliated with the company. It is an easy way to scroll through the upcoming auditions without any of the background information. If something looks interesting, check the Backstage website for more information or subscribe to the whole service.
Go to the My Entertainment World website, where auditions are listed by the month. The site lists some auditions up to three months in advance of the audition date. The vast majority of audition notices are for Equity auditions, so if you're not an Equity member, you might have to look elsewhere. My Entertainment World offers four different membership levels. A subscriber can join for one month for TV auditions only, or up to six months for film and TV options. Another option is NY Casting Calls, which maintains an ongoing list of upcoming auditions.