how hard is it to find a job after graduating from med school as a psychiatrist in big cities like nyc?

You don't graduate from medical school as a psychiatrist or any other specialist 

You graduate from medical school then apply for a position in a residency program when you complete that you apply for a job

You don’t graduate med school as a psychiatrist. You have to apply via match for a residency and you go where you match.  From there you will have resources and contacts for positions or you go into private practice and try to find patients

I don't personally know anything re: the "Student Doctor Network," but they have a forum of which questions related to medical school (and/or health-related professions) may be posted:

https://forums.studentdoctor.net/

Ask in education. 

not hard, just don't expect to make over $50,000