Damascus is a cool city. I spent three days there when I was in Syria. It claims the title of being the world's oldest continuously inhabited city, having said that so does Aleppo and Baghdad! It's also a Biblical city - Paul was blinded on his way to Damascus, and escaped the wrath of the locals by escaping in a basket lowered from a window.
All I can say is that the locals must have mellowed over the years, as they were all very friendly to me, wanting to know were I was from, how long I had been in the country and what I had seen.
The city is very easy to get around on foot, but if you don't fancy that, then there are thousands of yellow cabs that will take you where you want, and for next to nothing. Damascus is a city that you don't need a car in! There's also a lot to see, inside the old city walls near the Umayyad Mosque is the Souq - it covers a huge area and sells, well, it sells everything.
After all the hustle and bustle of the Souq, you can nip into the Umayyad Mosque to get away from it all, it's a great building, with a massive marble courtyard. You have to take off your shoes to go in, and the marble in the shade is freezing cold, and in the sun boiling hot - there is no middle ground!
The mosque contains two interesting shrines, the first in the mosque itself is the shrine of John the Baptist, they say his severed head is in the tomb. The second is just outside, and is the shrine of Saladin, the chivalrous leader who fought against the crusaders.
Another historical sight is "Straight Street" the street that follows the path of the old roman street right through the old walled city. It's mentioned in the Bible and it's not as straight as an arrow, but it definitely follows a line.