Some of the website I found for internships.
This link only provides information for some of the production companies there are, but if you click on the left side “Jobs & Training” it will take you to other links to an applicaiton for internships.
http://www.nyc.gov/html/film/html/discounts/production_company.shtml (for production companies)
http://www.nyc.gov/html/film/downloads/pdf/oftb_internships.pdf (for internships)
This is the internships for HBO. one of the places i dream to work at.
I am not sure about what kind of company it is, but internship sounds good.