The Historical Museum of Damascus is in an attractive old house with eight richly decorated rooms off a central courtyard. A couple of rooms hold displays of photos and diagrams relating to old Damascus, and there is a superb large-scale model of the Old City, but it's the rooms themselves, decorated in typical Damascene fashion with inlaid marble, carved wood and painted ceilings, that are of greatest interest.
The museum is off Sharia ath-Thawra, where the flyover comes down north of Sharia Souq Saroujah, beside two tall modern buildings. It's on Ministry of the Interior property and visitors have to pass through a guarded gate to reach the arched entrance.