Blue note gets all the tourist attention but the cover's ¥8000+ and honestly overrated. Better spots:

Cotton club in marunouchi. ¥4000-6000 cover but world-class acts and proper cocktails. Not just a tourist show.

Pit inn in shinjuku - legendary dive. ¥3000 cover, cash only, no talking during sets. Real jazz heads go here.

Jazz spot intro near kichijoji. Tiny basement spot, maybe 20 seats. ¥2500 cover includes first drink. Owner's been running it since the 70s and books incredible local talent.