Summer Housing for Non-NYU Interns

Hi, as the title states, I am a non-NYU undergraduate who is looking at potentially staying in the NYU dorms this summer. I am interested in having a single (without partial walls) in an apartment, but I also may be open to a traditional dorm.

How hard is it to get a single if you are not a student at NYU? Also, is there any dorm I should list as my top preference so that I will be more likely to get a single?