To be honest I am probably not the best person to ask about this… I am staying with my great aunt who lives in NYC. However I recommend looking into student housing for local universities, and looking online for students who are subletting for the summer. Students will usually put them up on craigslist (i know it sounds a bit sketchy but i know a couple people who have done this and its worked out) and on university run websites designed for students to put up info about their sublet. Also find out if you’re parents have contacts in the area, sometimes that can be helpful in finding a place to stay. My dad has a lot of friends in Brooklyn who sometimes sublet their places when they go out of town for extended periods of time. Unfortunately NYC is super expensive and I don’t think there is much of a way to avoid that… Hope this is at least slightly helpful!