Byblos (Jbeil), Lebanon is one of the world’s oldest continuously inhabited cities (settled ~8800–7000 BCE), but it is not the oldest.
Damascus, Syria has evidence of continuous habitation from at least 9000 BCE (possibly 11,000 BCE), making it the generally recognized oldest continuously inhabited city.
Other contenders: Jericho (West Bank, ~9000 BCE), Aleppo (Syria, ~8000 BCE), Plovdiv (Bulgaria, ~6000 BCE). Byblos is a close runner-up and a UNESCO site.