I visited Sarajevo in March and April 2015
Bašcaršija (I never managed to pronounce the name properly on my trip), lies in the old town of Sarajevo. It is an old Ottoman market, and dating back to the 15th century, it is as old as the city itself.
Among its many sites is Sebilj, situated on Pigeon Square, a wooden fountain that can trace its origins back to 1753.
Before, the market had different streets devoted to different trades, today only the coppersmiths’ street survives.
A popular souvenir to buy is a hand-made Bosnian coffee set.
A visit to Bašcaršaja, while in Sarajevo, is greatly recommended. There is plenty to see; mosques, old inns, streets still looking hundreds of years old, souvenirs and real Bosnian crafts. Many parts of the market still retains some of that Ottoman feeling.
And if you get tired you can always stop in one of the many bars or cafés here, for a coffee, beer or Nargila, and maybe a friendly chat with the locals. Most cafés and bars here have wi-fi as well.
My personal favorite is Tunis Bar, only about a hundred meters from Pigeon Square. A small bar, not too noisy, but with friendly staff and a great atmosphere.