The heart of the city is its ancient Casbah, a steep and narrow maze of streets just west of the Pl des Martyrs. There are several magnificent Ottoman palaces to explore, most concentrated around the Ketchaoua Mosque at the end of Rue Ahmed Bouzrina; the finest is the Dar Hassan Pacha. Above the medina is the city's Citadel. It's been closed while undergoing major renovation for several years, though it's still possible to skirt its rambling exterior.
This fiercely traditional neighborhood saw some of the bitterest fighting during the Battle of Algiers (Gillo Pontecorvo's extraordinary film of the same name was shot in situ shortly after the war's end). The Casbah is fine to walk around today, but exercise extreme caution with personal belongings and avoid going there at night. Hiring a guide (ask at your hotel) is not a bad idea.