Bourbon Street is the loud tourist strip; the live music people actually go out for is on Frenchmen Street and uptown, generally starting late evening and running until the band stops.
Preservation Hall
726 St Peter Street in the French Quarter: traditional New Orleans jazz played acoustically in a small room, several short sets a night from around 5pm, roughly 360 nights a year, drawn from a collective of 50-plus local players. Reserve through the venue's calendar — walk-up space is limited.
d.b.a.
618 Frenchmen Street, open daily 6pm–1am and from 2pm on Saturdays. Live music most nights plus a beer and whiskey list that is reason enough to arrive before the band; cover depends on the act.
The Spotted Cat Music Club
623 Frenchmen Street in Faubourg Marigny, open 2pm–2am daily. Trad jazz, blues, funk and klezmer in a room about the size of a living room; strictly 21+ with a US photo ID or foreign passport (photos of IDs are refused) and a one-drink minimum. Go early or expect to stand.
Tipitina's
501 Napoleon Ave uptown, a ride out from the Quarter. Touring and local acts across brass, funk and rock, plus a Free Friday Concert Series that is the cheapest good night out in the city.
Maple Leaf Bar
8316 Oak Street uptown, one of the city's longest continuously running live-music rooms, with something on most nights: rotating local line-ups Tuesdays, an organ-led Wednesday with Joe Ashlar and Stanton Moore, and Josh Paxton's Booker & Beyond on Thursdays.