This can be tricky to ascertain, especially given the nature of archaeological inquiry and the historic unrest in the regions where many of the oldest cities are located (consider Aleppo, for example).
Damascus is considered to be the oldest continually inhabited city in the world, although there are several other cities in that general region of the world that are also extremely early. Jericho and Aleppo are other early contenders. Jericho is said to be the oldest walled city at the very least.
Some sources: