It's been a few years and, at one point, they were doing renovations but I've definitely hung out in the Rose Reading Room at the NYPL in the past. And there's nothing on the NYPL's current site to suggest it's not open for just sitting and reading.
If I’m coworking in NYC sometime, maybe I’ll ask what kind of research I must be doing to get to read there. I’m guessing with the physical books only available there?