Arabic is the official language. It is always a good idea to know some words ("hello", "thank you" etc.). A surprising number of people speak at least (very) rudimentary English. It would however be worth your while to learn basic numbers in Arabic in order to negotiate taxi fares. Personnel working with foreign tourists (like tourist hotels, restaurants, tour guides, etc.), generally can communicate reasonably well in English.
Due to the general lack of ability by the public at large to communicate in English beyond basic phrases, Syria is a great place to force yourself to learn Arabic through immersion, should you wish to improve your Arabic skill.