Final answer:
Andrea Palladio worked primarily in and around Vicenza, where he designed classical buildings like Villa Godi Valmarana and the Olympic Theatre, contributing to the development of Palladian architecture.
Step-by-step explanation:
Andrea Palladio, a renowned Italian architect of the Renaissance period, performed most of his influential work in and around the city of Vicenza.
One of the hallmarks of Palladio's architectural style is Villa Godi Valmarana, located in Lonedo di Lugo, Veneto, Italy. Its classical features, including a symmetrical facade and arched doorways, are a testament to Palladio's adherence to classical stylistic values. Furthermore, the Olympic Theatre in Vicenza stands out as a significant work by Palladio, designed in 1580 and completed posthumously in 1585.
This theater's inauguration with Sophocles' 'Oedipus The King' marked an important cultural event. Palladio's influence on architecture extended throughout the region, leaving an indelible mark on the principles of design and aesthetics rooted in the classical traditions of ancient Greece and Rome, laying the foundations for what would be known as Palladian architecture.