Why was Athens an important place in ancient Greece?

Answer 1

When peace was made with the Persian Empire in 449 BCE after 50 years of war, Athens seized the funds of the anti-Persian Delian League and continued to enforce annual payment of the war levy by the cities of the League.

It used this money to sustain the war fleet which continued to collect the money, and used the funds to glorify the city (build the Parthenon etc), to put half its own populace on the public payroll, entice the best artists and other performers and philosophers and natural scientists etc to Athens.

It became, for a half century, the centre of the Greek world, however its hubris caused it to over-reach itself in the disastrous 27-year Peloponnesian War against the southern Greek Peloponnesian league led by Athens. It lost in 404 BCE, was stripped of the empire it had created out of the Delian League, and without the money it extorded from that empire, sank to being a second-rate power.