It's as safe as any other big city. The quarter has never been dangerous. If you like to wander around dark, bad neighborhoods at night you might want to go someplace else 😀
Stay out of North side downtown [i.e. Jefferson Parish]...just saying. I lived there for 6 some odd years and it wasn't tourist ideal way back when and def not now. Also check out Algiers and Gretna....🙂