Specialty Shops in NYC

Eataly is pricey but fun, even just to people-watch!
Gulluoglu Baklava Cafe is at 52nd and 2nd, and a fun place to get simit (like a cross between a bagel and a croissant) and a wide selection of filo pastries. I think they have other breads too.

Sahadi's in Brooklyn Heights, and also stop next door at Damascus, the guy is incredibly nice. Kalustyan's in Murray Hill (Manhattan). Also make sure you go to the Chelsea Market, they have many specialty vendors, but make sure to check out Seed & Mill for tahini and halvah, and also Spices and Tease, for (duh) spices and tea. Actually Chelsea Market is a great resource for specialty foods, so make sure you walk around.

Also Kalustyan's in Manhattan, Bklyn Larder and Greene Grape Provisions are all really nice. Bklyn Larder is a great spot to buy bread, and Klustyan's is huge and has everything you could possibly want/need/imagine.

You MUST go to Sahadi's in Brooklyn Heights! (http://www.sahadis.com/) They have an amazing selection of (affordable) cheeses, spices, sauces, and lots of treats! Check it out!

Clarification #2:
As someone who's usually underwhelmed by the averaging nature of sites that compile "the best" on aggregate I was hoping that there would be enough NYC folks here on the hotline to get some really specific recommendations. A sharing of secret spots if you will. And Specialty doesn't need to be an international market, if you know a place with great fresh pasta, PLEASE let me know! (We've been trying to figure out if there's any counter/table in her appt. on which I could clamp my pasta machine... Since not *quite enough* space is a common problem in the city, I'm hoping there's lots of recommendations on where people go to get something that is just too difficult to make at home).

An example from my life. When I want to make falafel, theres a specific latino market in town I check first because more often than not they have fresh (green) chickpeas. They also have the best fresh masa within a half hour drive from my house, though it is incomparable to what you can find in the central american neighborhoods a little closer to DC.

Also, when looking at chowhound or other sources, think of specialty foods that you cannot get at home, or whose quality you cannot get. Examples: spices, exotic ingredients or liquers, depth of holdings in some wine stores, kitchen equipment, especially in commercial supply stores.

You might check out Chowhound (chowhound.com); they have local message boards for various locations, and can be useful for this sort of question.

Where about in Brooklyn? It's a very big borough.