It's difficult to name just one state. The category of "most important" is a fuzzy one: do we mean the state we know most about, or the biggest or richest one, or the one that was the birthplace of an unusual number of philosophers and artists, or the most powerful one, or some other measure? In almost all imaginable categories, in the Classical period (479-322 BC) Athens would rank first. In some categories Sparta would be second. But already there would be rivals for second place; Sparta may have been the top contender for most powerful and wealthiest state, but it certainly wasn't second in the number of its citizens or its cultural prominence or the size of its army. So how do we determine which was the most important?

From a historical perspective, the most prominent and highly regarded state after Sparta would almost certainly be Argos, its chief Peloponnesian rival. The territory of Argos included the ruins of the Mycenaean centres at Mycenae and Tiryns, so that Argos could claim to have been the dominant power in Greece in the Age of Heroes. Argos was also one of the largest and most populous states of the Greek world. Despite many wars against Sparta, neither side ever fully managed to subdue the other; even when Sparta was the hegemonic power in mainland Greece, Argos was at best an unwilling ally, and often claimed neutrality in Sparta's wars against others. Throughout the Classical period Argos remained a thorn in Sparta's side and an invaluable ally for any who wanted to challenge Spartan power.

Other states were great too, however, and by the Classical period many overseas settlements could rival the size and wealth of the cities in Old Greece. Culturally, there was no match for the importance of Miletos on the coast of Asia Minor, which served as a centre for the exchange of ideas between Greece and Persia, and which also got to claim the status of founder for innumerable overseas states (regardless of whether it had actually played a role in their establishment). In terms of size and wealth, few cities on the mainland could rival Cyrene in Libya or Akragas on Sicily (until Carthage destroyed it in 409 BC). In later periods, the Spartan colony at Taras (Tarentum) would grow to be one of the most powerful cities in the Greek world.

But the real contender in the Classical period was Syracuse, a Corinthian settlement on Sicily that ranked second only to Athens in the size of its territory and people, and would only grow further in the Hellenistic era. Syracuse was one of the only states to be able to rival Athens at sea without foreign financial aid, as well as matching some of the largest hoplite and cavalry forces of the Greek world. Thanks to its close ties with other Western Greek states, it was also a centre for the development of new forms of philosophy and theatre. By the end of the fourth century BC it was a hub of trade and culture from which Greek settlers ruled nearly all of Sicily.

In terms of religious significance, no state could hold a candle to Delphi. Greeks and non-Greeks from all over the Mediterranean came to Delphi to hear the advice of Apollo and to dedicate riches to him (displaying their wealth and prowess in the process). The authority of the oracle and the wealth of the sanctuary translated to political importance as well. Since Delphi was a small and remote community in the larger region of Phokis, it could do little to defend itself from encroachments by larger powers; instead, a group of Greek states known as the Amphyktionic League were sworn to protect it. In the Classical period at least 2 wars were fought over control of the sanctuary.

In terms of naval reach and empire, the chief rival of Athens for most of the fifth century BC was Corinth, the old mercantile state that challenged Athenian power both in the Ionian and the Aegean Sea. The first great wars of this century were effectively fought between Athens and Corinth for naval supremacy, even if Sparta was nominally involved as the hegemon to which Corinth was a subservient ally. Corinth had been great in the Late Archaic period, but in the fifth and fourth centuries BC it became overstretched and exhausted from constant wars. Its lacklustre track record in the First Peloponnesian War and the Archidamian War were signs of its decline, and its key strategic role in the devastating Corinthian War (395-386 BC) sealed the deal; Corinth was unable to keep up with Athens at sea or with Sparta on land, and ended the period as a second-rate power.

Thebes had the opposite trajectory, starting the period as a relatively minor city with a bad reputation for submitting to Persia, but growing gradually in wealth and influence as Spartan power waned. After the spectacular victory of Thebes over Sparta in the battle of Leuktra (371 BC), Thebes briefly became the most powerful state in mainland Greece, prompting Athens to seek an alliance with its former enemy against the new kid on the block. But Thebes had neither the people nor the wealth of a place like Athens, and its ascendancy did not last. By 362 BC it had lost its most prominent general and was forced to mostly abandon operations on the Peloponnese. In 356 BC it became involved in a war of attrition against its neighbour Phokis (incidentally, a war over control of Delphi) which was ultimately settled by Philip of Macedon ten years later; the subjection of Thebes followed in 338 BC. The city rebelled in 335 BC, but Alexander the Great marched down with unparalelled speed, seized the city, and razed it to the ground.

By this time, as the Greeks themselves were well aware, most of the once-great cities of Old Greece had been humbled by war. Sparta was a second-rate state; Corinth was out of the game; Thebes and Argos were unable to make good on their lofty claims. Athens was the only city that seemed to be able to absorb every setback and still grow richer. But by this time states like Syracuse were arguably greater, and the centre of the Greek world had moved away from the mainland.