Baščaršija is the Ottoman heart of Sarajevo — a quarter of cobblestone lanes, courtyard mosques, copper workshops, and cafes that has been trading since the 16th century. It is touristy in places but not fake; this is a living market quarter, not a reconstruction, and the coppersmiths still hammer out džezva coffee pots and round trays the way they have for centuries.
The Sebilj fountain in Pigeon Square (Trg Oslobođenja) is the symbolic centre. Walk out from it in any direction and you'll pass mosques, hans (old inns), craft shops, and cafes selling Bosnian coffee in traditional copper sets. The surrounding grid of lanes reflects the original Ottoman guild organization — separate streets for leatherworkers, goldsmiths, and textile merchants. Budget several hours to wander properly; the best parts are the back lanes away from the main shopping streets.