One of the things you should do when you visit Turkey is to drink a traditional Turkish coffee. It's strong and different from the coffee you taste or drink at home, but it's a "must" to try for every visitor.
Best places to drink a coffee in Istanbul is the Pierre Loti Caffeteria in Eyup. In the countryside you can have it in local coffee houses.
For more information on Turkish coffee see this page: https://www.allaboutturkey.com/kahve.htm
In 2013 Turkish coffee entered the UNESCO's Representative List of the Intangible Cultural Heritage of Humanity. For a full list of Heritage in Turkey see this page: https://www.allaboutturkey.com/heritage.htm
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