Piraeus is the seaport for Athens, the capital of western civilization, which boasts a fantastic mix of classical ruins and vivacious modern life. In a single day, you can climb the hill of the Acropolis to wonder at the Parthenon, join the lively Athenians in Constitution Square, and then find a welcoming taverna for some spirited bizouki music, plenty of ouzo to drink, and with luck, energetic Greek dancing.
Catch the X-80 bus outside the cruise terminal--4 euros for a 24 hour ticket--for an express ride to the Acropolis. The same ticket takes you back to the cruise terminal; buses run every 30 minutes.