Museums related to music and Black experience in New Orleans:

Ashe Cultural Arts Center - https://www.ashenola.org/
New Orleans African American Museum - https://www.noaam.org/visit
Black owned and led Tours - https://www.knownolatours.com/ - Treme Walking Tour
New Orleans Jazz Museum -run by the State - https://nolajazzmuseum.org/

New Orleans has a bunch of good record stores. I am big into vinyl myself. I am a fan of Peaches on Magazine Street, Euclid Records and Domino Record Shack. They all specialize in different things but are run by knowledgeable people with a solid collection of local artists and rarities.

Also, if you are into New Orleans vinyl, join https://tipitinasrecordclub.com/. Trust me, worth every penny.