Decided to power rank the ones I've been to because I'm 9 hours deep sitting here.
This is really long but I felt inclined to pen this because I am procrastinating.
I recommend numbers 1-5.
1. Seward Park: Upstairs is perfectly very quiet and has nice window views...it gets great afternoon sunlight too, second floor has really cute children, Seward Park itself is really nice outside to take a break, great coffee nearby at Little Canal, bathroom on the first floor, really pretty building, this is my top pick.
2. Jefferson Market: Upstairs is sufficiently quiet to get work done, the building itself is truly gorgeous inside and out, bathroom in the basement, open later than some of the others, overflow seating in the basement but ngl you want to sit upstairs, minus points for some tourists coming in which kills focus.
3. Greenpoint: This is technically Brooklyn Public Library (different than NYPL) but still on my list, this branch is so gorgeous and the most modern branch on the list, really cute kids here too, super clean, highly recommend to the Brooklynites among us.
4. Tompkins Square: Casual branch with less seating and a little more noise, great location right next to Ninth St Espresso, good for a short jaunt to browse the books or get an hour or two of work done, major minus for having no bathroom and for not opening until 11am on some days of the week.
5. Ottendorfer: Hidden gem in a building you would not know is a library, good central location, minus points for very slim seating and for not opening until 11am some days of the week.
6. Mulberry: Good local spot amongst the hustle and bustle of Soho, not much else to say here, need to explore more...but there must be a reason I don't go back.
7. Stephen A. Schwarzman / Main branch: It's over-touristed and it's in midtown. Only go here as someone visiting from out of town who is into a museum vibe.