Well, not Americans anyway. This is from the US State Department. ENTRY/EXIT REQUIREMENTS: A passport and a visa are required. Visas must be obtained prior to arrival in Syria from a Syrian diplomatic mission located in the traveler’s country of residence, although the Syrian visa policy with respect to American diplomats and citizens is currently under review.
And I know from experience that the visa is about $100 USD but as you say, well worth the price. Damascus is a fabulous city.
Mandi