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The Scene – The three tastefully decorated rooms offer the cream of the local musical crop, including jazz, blues and R&B, starting in the early afternoon. The environment is meant to evoke the fabled red-light district from which the club takes its name, but that's as close as you'll get to the often-crass commercial maelstrom of the French Quarter at this first-class establishment. – – The Draw – This ambitious complex offers the best of both worlds, on a scale unmatched by any other club or restaurant. Most nights feature a dinnertime "jazz jam" with a rotating…