Now that I'm in Syria, I found out the following:
If you have a card which is connected to the Maestro Network, there are only few places in Syria where you can get cash. At most ATMs you will just get error messages.
I was successful at two different branches of Banque Bemo Saudi Fransi and a branch of Audi Bank. I assume that all of their ATMs do give money to holders of Maestro Cards.
These are the location where I successfully got money:
- Aleppo: Banque Bemo Saudi Fransi: About 200 m north of the Great Mosque. If you go there from the clock tower, go south until Sh al-Mutanabi, then turn left (east) until the traffic circle. It's about a hundred meters south of the traffic circle on the right side of the road.
- Hama: Banque Bemo Saudi Fransi: Just north of the clock tower on the east side of the road.
- Damascus: Bank Audi: On the south side of Saahat Yousef al-Azmeh in Central Damascus.
Hope that helps.