Beer Good,
Just a quick answer without time to fill in the details right now. There's:
Coliseum Books on 42nd street across from the Library, very large.
The Strand Bookstore, way down town on about 10th and Broadway, huge collection of used, all sorts, jammed in everywhere. Possibly analogous to Powell's.
The Gotham Book Mart on about 47th off Fifth Av. is a rare kind of smaller store that deserves a look-in (and homage). Not many like it left, fighting off the dominance of B&N in B&N's home town.. The kind of specialized treasure that you find (only?) in NYC. At least read about it on the Web.
I should also mention the Argosy, 'way over on the East Side, but I haven't been there in a long time
And down around the Strand you might still find all sorts of very small dusty book shops you might stick your head into if you are venturesome and want to explore or see what one looks like.
The main Barnes and Noble on about 17th Street and Fifth avenue, is the original flagship store that started it all and has a
huge selection, including an overwhelming number of text books. Every college student knows of it and goes through there at some time or other. It is worth a look. The B&N not too far away, perhaps on 8th avenue, is a modern store and not very small either, possibly with a more general selection than the main store. CD's galore.
BTW the Four Continents Book Store devoted to Russian is not so far away, I believe that, in the day, it was the only authorized outlet for Soviet literature/propaganda into the US. [!}
You should be able to find Web pages for all of those mentioned.
If you happen to get up around Columbia University, (116th and Broadway) then there (probably still) is Salter's, another venerable landmark from my early days, and I'm pretty sure the University Bookstore across Broadway is available to the general public as well, with a varied selection, as well as texts for all courses.
When are you leaving? In case I can scare up more detailed information.
Any specialized interests? There are probably individual bookshops for them also. New Yorkers say "New York has it all," with pardonable pride. and really pretty fair accuracy.
Any questions I can answer?
I'll be out the rest of the day but back this evening.
Enjoy the browsing,
Peder
PS Shakespeare's, by name but with general selection, may still exist, but may well have succumbed to B&N I seem to remember hearing. Scribner's on Fifth in the Fifties is probably long since gone, having succumbed to a large new B&N across from it I also seem to remember hearing.
P.
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