in New Orleans, THE long-running place for jazz of the straightahead/modern/mainstream variety is Snug Harbor on Frenchmen Street.
www.snugjazz.com It's home to pianist Ellis Marsalis, who often plays in a trio with son Jason on drums. Astral Project (with great bassist James Singleton) plays there from time to time, and so does pianist Henry Butler. It's a small place, with tables, and more popular acts will sell out. Frenchmen Street is a great place to hang out, because there are so many music clubs happening in that area - funk, jamband, blues, reggae, more. The Blue Nile is always fun.
Just opened, at the Royal Sonesta Hotel on Bourbon Street, is a mostly straightahead and traditional club operated, in part, by trumpeter Irvin Mayfield (Los Hombres Calientes, etc.). Lots of great players come through that club.
Of course, there are tons of clubs around NOLA that feature all kinds of jazz- or jazz-related music, like jazzy jambands, brass bands, etc. The Maple Leaf, uptown in Carrolton, is a great place. Not too far away is Mid-City Lanes Rock 'n' Bowl, a great place to visit, recently relocated to a new, more spacious facility. It's basically a '50s-style bowling alley with a concert stage. So is Tipitina's (uptown).
For info/schedules, Offbeat Mag (
www.offbeat.com) is a great source, and so is the weekend mag put out by the Times-Picayune (
www.Nola.com). Gambit Weekly has listings, too.
Look for any appearances by bassists James Singleton or Roland Guerin. And drummer Stanton Moore, when not on tour with Galactic, plays with a bunch of jazzy, funky side projects, most worth hearing.
I'm sure the NOLA-based folks will chime in with more suggestions. I'm just a frequent visitor (& big Jazz Fest fan).