Virtually every country that produces livestock (cattle, sheep, goats) also produces cheese. That is why there are so many varieties of cheeses around the world. May I suggest including cheese-tasting on your travels. There's nothing quite as authentic about experiencing a new venue than stopping at its local delicatessen or butcher shop for a hunk of cheese to go with local breads and wines. These are the foods that most often define a region or town in the Western Hemisphere.
And while cheese doesn't seem to have caught on in Asia, it is a staple in the Middle East. If you haven't tried cheese tasting, start today. I put Feta cheese on a salad this week for the first time...
It used to be fairly close to Washington Square, at 6th Ave and 9th Street, but has moved quite a bit farther away these days. It's now at 14th Street and Eighth Avenue.