It's funny -- you can trace the "1920s Paris scene" through the century til sometime in the '90s, at which point major cultural centers stopped coalescing in that fashion. Many reasons for that.

For instance post-1930 you've got Sartre's scene, Hemingway's Cuba, then later Beatnik San Fran and New York, Berkeley (the famous "high water mark"), briefly Aspen, Greenwich Village, the London New Romantics, maybe Seattle. Mostly revolving around music and a certain lifestyle, but definitely some literature. The arts in general. Now ... Brooklyn? Brooklyn's kinda gone off the rails and it's sure as hell not cheap. I think it's the closest you're going to get.

Good question.

(As far as primarily literary scenes ... the modern publishing industry destroyed literature.)

Preemptive edit: it may seem like I largely dismissed the rest of the world -- but I think the 20th century, as far as cultural movements in the sense that you mean, was essentially western. It was in a lot ways the century of the West, and the one we're in right now is most assuredly not. Maybe the next great literary/musical/artistic scene springs up in Singapore or Hong Kong or Joburg.