Which of the Greek city-states from the Classical Era would have the best chance of uniting the Hellenes across the Mediterranean under one flag? Corinth, Athens, or a reformed Sparta?
Athens, followed by Corinth. Sparta was inhibited from this sort of power projection if for no other reason than its insanely vulnerable strategic position and limited demographic base. Thebes lacked any interest in this sort of expansion (generally didnt act outside of mainland greece), and there are not very many other alternatives. Athens is a better option, simply because it tended to be more powerful than corinth (alliances with Sparta excluded).
But the idea of an united classical greece is a little far-fetched. The polis were so fractured that any one state which tries to exert true hegemony is going to be resented and, sooner or later, challenged. Athens, Sparta, and Thebes all rose and fell in the course of a century. One possible option would be a far less successful Alexander, who establishes some broad pan-Hellenic ideals but then dies, leaving Macedon in disarray.
Athens steps into the power vaccumn caused by the destruction of Thebes, and reestablishes itself as the leading city-state.
However, a more divided greek speaking world is more likely to occur, regardless of POD. Probably the best that you could realistically expect would be for a multipolar greek world, with several polis each having their own spheres of influence. Syracuse dominates Sicily, Italy, and the western Mediterranean, Sparta reigns supreme in the Pelleponese, Corinth holds the isthmus, Argolis, and perhaps some colonies on the gulf of Tarentum/Adriatic coastline, Athens controls Attica and the Aegean, Thebes dominates Boeotia, etc...