Finding an apartment in New York is, pardon the hyperbole, LITERALLY THE WORST.
Only in New York will real estate agents, Craigslist and "friends of a friend" think it's acceptable to trick you into living in a windowless box for $3300/month.
Here are the best ways to find an apartment in NYC with advice from real-life New Yorkers who've gone through the struggle, so you don't have to.
Zumper is cool because you can get a free Experian credit report* AND fill out an application to keep on file for when you're ready to apply for an apartment.
*This kind of credit report is called a "soft pull" and won't affect your credit score.
2. Pad Mapper
CRAIGSLIST! Frequently this site is just a giant garbage bin, but you can actually find an apartment here (it's where I found mine).
Consider looking at listings with no photos (many landlords just don't have the time/energy/technological skills to take pics) for the best deals. It's definitely a "you have to kiss a few frogs to find a prince" type situation, but there is definitely gold to be discovered.
Naked Apartments is a standard "I want X for $X/month" type of search, but their listings are pretty good.
They also have a cool feature where you can enter in your price range and number of bedrooms and they will generate a map that tells you where you will have the best luck.
7. Street Easy
StreetEasy has one of the largest selections of apartments. Requires some sifting for sure (especially since lots of "featured" units are placed at the top which don't exactly match your search), but I know many people that have had great luck on this site.