The vacancy rate in Manhattan right now is 1%, and the summer has not even started! You will rent quickly, within a week, if the property is desirable and the rent is right.
If I were you, I would get the help of a real estate agent. You want someone who will provide a legal lease, all the required disclosures, obtain credit checks, etc. As a former journalist I personally verify employment and references of tenants for my clients by phone, I don't rely on paper information. Feel free to contact me if I can help.
Licensed Real Estate Salesperson
New York, NY