What city became the center of the musical activity in the classic era?

Vienna, Austria. The Classical Era in its strictest sense is even referred to as Wiener Klassik (Viennese Classical) in German, especially when distinguishing it from the Baroque Era (eg. Vivaldi, Handel, Bach) which preceded it, and the Romantic Era (eg. Brahms, Schubert, Liszt, Wagner), which followed.

The majority of the great classical composers, such as J. F. Haydn, W. A. Mozart and Ludwig van Beethoven among others spent significant parts of their careers in Vienna.