Which city was a key cultural center of the most advanced civilization of the classic period ?

Teotihuacan.

Explanation:

The Classic period was considered a trade mark of the cities of Mayan culture.

This period took place in 250 AD to 900 AD, and all the achievements of arts were achieved by the Mayan civilizations in this period.

Here's a timeline:

400 AD -- Teotihuacan became the dominant city that had power over Mayan's mountains.

560 AD -- Tikal city was conquered by the union of other city-states.

600 AD -- Teotihuacan stopped being the center of cultural events.

900 AD -- Teotihuacan gets abandoned. The end of Maya Classic period.

Archeologists and other people still know very little about those events and why this period was ruined and over, it all still remains a mystery.