When to start looking for housing NYC ?

Realistically there will not be any July listings until May at the earliest and most won't appear until closer to June. I would use this time now to identify 1) roommate(s), 2) neighborhoods you are interested in, 3) housing budget, 4) must-have amenities, and 5) the rental/broker process and needed documentation. The best apartments will go under contract the same day they are posted during the summer. Prices are also generally higher during the summer than what you are looking at now.

I would not rent a unit without viewing it first. Once you identify/grasp the above, I would pick a few days in late May or early June to visit the city and tour units/neighborhoods with your roommate(s). You should aim to sign a lease during that trip (i.e. have your documentation and money ready to go).