No question about it, you will be walking a tighter timeline than you may be comfortable with when searching for a rental apartment in the New York City. 

Apartments are typically listed just 30-60 days in advance of the date they become available, so it's tough to begin your search farther out than that. There will be many more listings available 30 days in advance than 60.  Expect to spend anywhere from three days to three weeks on your rental search.