The Eixample holds a ton of great places to experience Barcelona culture. The National Symphony of Catalonia is based out of L'Auditori, a modern concert hall with excellent acousitcs. Alternatively, the Fundació Caixa always has an interesting activity or event planned. Cinema fans will find 4 art house movie theaters and music lovers can head to a number of great locales, such as La Boite or Luz de Gas.
Even though the Eixample is a more upscale neighborhood and not known for being particularly "hip," it's certainly got a stellar cultural offering.
Where to experience Barcelona culture around L'Eixample:
Movie Theaters (original version with subtitles)
For complete Barcelona culture listings (address, telephone, metro, etc.), click on the title links of each section above.