Not a cafe, but the Rose Reading Room at the 42nd St. library is the prettiest, most productive place to get work done. Also easy to move outside to Bryant Park when it's nice out.
The lesser known but very nice alternative is SIBL: Which has nice workspace in its lower level reading room. This is more quiet like a university, and not like a hip/trendy etc. But they also have photocopy, print, and research materials if you should need some.
NYPL: Science, Industry and Business Library (SIBL)
A good choice however you are not allowed to consume your own food/water/coffee there. So if you have something you need to do in two hours or less with no breaks, then this is a great place.
How loud is it there? The stone walls and tile floors make me think it's very live, acoustically speaking. Are people quiet enough that it's not a problem?
(edit): Looks like it's nearly unanimous. Here's a picture for folks who haven't been there: http://nycpano.files.wordpress.com/2011/03/rose-reading-room...