Cooper Union’s admit rate for architecture is around 4%, though, so it should be considered a reach for any applicant. They have a particularly interesting application process, where applicants have around one month to complete and submit a studio test.
We toured it briefly a while back. It’s basically adjacent to NYU/between the NYU departments and some of the dorms. Definitely a vibey part of the village to be in. If I recall correctly, no one is guaranteed housing and only first years generally get any, so the costs of renting /sharing an apartment in NYC do need to be factored in.