Sang-e Siah — the "Black Stone" district — is the historic core of old Shiraz, a tangle of mud-brick alleys, low arches, and quiet courtyards stretching west and south from the bazaar. Many of the houses are abandoned or partially ruined, but a slow restoration effort has converted some of the best into boutique guesthouses, cafés, and craft shops.
The whole quarter is a pleasant walk. Lose yourself in the alleys for an hour, look for the carved wooden doors and the painted plaster above the entrances, and stop in at one of the courtyards converted into a teahouse. The Pink Mosque sits on the edge of the district, so it is easy to wander into.