The Black Sun Jazz Club doesn't feature live music despite its name. It's a split-level bar owned by the extremely mellow Ujiie-san. He's what most people would imagine a Japanese jazz bar owner would look and sound like; turtle-neck, low-voice, chain-smoking, unflappable.
The entrance is on the second floor, which opens into a very small space packed with bottles, cds and a couple of chairs along a counter. The very steep stairs on the left lead up to a slightly bigger room fit for a group of customers. The music perfectly fits the interior of the bar, all modern jazz with an emphasis on moody instrumental stuff based on what I heard. Gerry Mulligan's "Night Lights", followed by some slow-burning Herbie Hancock tune.
Ujiie-san said he usually closes around 1am but often keeps it open past then if there are customers, so if you see the sign lit up at any time of night he should be there.