Recommended accom. in Syria - Damascus
 

Places I've stayed at in Syria where you can park your bike indoors.

Damascus
In Damascus I can recommend staying at the Al Haramein. It's a typical backpackers place, central and fairly cheap. They will let you park you bike safely in their garden if you ask. A dorm bed was 500 s.p in dec 2010.
Address:
Sarouja Bahsa St Damascus Syria
Tel: + 963 11 2319489
Fax : +963 11 2314299

Deir Mar Musa
The monastery 80km north of Damascus has a garage where you can park your bike during the night.
Def worth a visit.