If you want to experience several festivals in a week, spend that week in Barcelona since they have the most varied and extensive number of festivals in all of Europe, encompassing different fields of entertainment, including theater, dance, film, music and video.
Examples of the festivals that you should see are the Sonar Festival of Advanced Musics and Multimedia Art, the Barcelona Guitar Festival, the Festival of Contemporary Music, the Festival of World Music, The Vella Flamenco Festival, the Festival of Opera at Butxaca, the International Festival of Visual Theater and Puppets, the Barcelona, International Jazz Festival, as well as the Alternativa International Festival of Independent Film.