Test Pattern posted:

Museums. We have a lot and most of them are great. Lesser known and good: art: Frick, whitney, MoMA PS1 in LIC, Brooklyn museum, folk art, cloisters; cultural: museo del barrio, Jewish museum, native American museum at the battery, and on and on (whatever your ethnic backgrounds and interests, there's likely to be at least one museum laser-targeted for you in the city)
Only bookstore worth going to as a tourist (unless you have a special interest in one of the specialized stores that remain) is Strand. With Kim's gone, no movie store is worth visiting as a tourist.
Cafes, there's at least one somewhat cool cafe or cafe-likw space in almost everyneighborhood .

The problem with recommending anyone anything is there's something for everyone. Into film? Museum of the Moving Image, good indie cinemas in Manhattan and Brooklyn. Into cafe culture or coffee conneisurship? Cafes for both of those.