I quickly googled for old clocks and found:
-The oldest astronomical clock in Lyons, France (1393)
-The oldest clock in Comayagua, Honduras (made by the moors, donated by the king of Spain, 800 years old)
I stopped there, first because I suspected that I would find a lot of “oldest clock in the world” (a quick glance shows there are at least two of them in France alone), but more importantly because I found a reference to something which has a chance of be the oldest clock which could still be used. A 3500 y.o. clepsydrae kept in the Cairo museum. But I suspect it isn’t what you’d call a “machine”.