Housing advice for summer internship in NYC?

Does anyone have advice on a website that lists all the options or if you have advice on where to start. Just call each of the schools in Manhattan?

Does anyone know if it’s a scramble trying to get a room / got to be first on the list to have a chance? or there’s loads of supply? Hoping for something walkable or just a short subway ride from Times Square area.

Thanks!

Search for 92Y residence

Check some school’s websites. NYU has a page about summer housing.