The Old Town of Damascu is no doubt the hightlight of your journey to Syria!
What I enjoy most is having a walk around the Old City. When you get away from Umayya Mosque and bazaar streets, you will find a different world. There is quiet and tranquility. Get lost in the labyrinth of the narrow streets - that's the best adventure!
The Old Town is divided into different parts (Bazaar, Muslim, Christian, Jewish). Each of them is worth wandering.
After dark, the streets are maybe even more magical. Don't be afraid--it is safe here!