There is not much to see in Taksim Square (Taksim Meydanı or Estambeyoğlu) really except for the monument in the middle.
However, there are 3 things that you need to know about Taksim if you are visiting Istanbul in the Beyoglu part. For those who do not know, Beyoglu is the modern part of Istanbul located in the European side, just off the Galata Bridge across Fatih, the historical area of Istanbul. Beyoglu is where you need to go in the evening when Fatih shuts down.
Here are the 3 things about Taksim:
1. Taksim is where you can find cheap kebabs. Just across the square on the corner of Istiklal Street you will find a line of kebab stalls. Döner kebap! I made a post about the street foods in Istanbul which includes the kebabs here: A List of Street Foods (and Fast Foods) in Istanbul
2. Taksim is where the connection to the Metro is located, underneath it. The Metro is connected with a funicular that runs between Taksim Square and Kabatas on the waterside. From Kabatas you can take the metro to Fatih, the historical part of the city.
3. Taksim is where all political demonstrations are held in Istanbul. Stay away from this area if there is a demonstration. If its a very important demonstration, the police will cordone the whole area, and sometimes including the surroundings, such as the busy Istiklal Avenue.
This is what happened when I arrived last year in May (on Labor Day). My story here: First Few Hours in Istanbul – Police Barricade, teh Frenzy, Turkish Mezze and Meeting a Couple from New Zealand
Travel Period: May 2015
Destination: Beyoglu, Istanbul (Marmara), Turkey
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Happy Travels! Enjoy Life =)