I’d also recommend the Kitano and the Cornelia Street Café. My absolute favorite place to hear jazz is the Jazz Standard.
If you are into big band, you may want to try Swing 46. On Monday evening’s you can hear the Harlem Renaissance Orchestra perform.
The Cornelia Street Cafe 2006 The Kitano New York Hotel, Kitano Hotel New York, Kitano.com Swing 46 Jazz and Supper Club - Calendar,
//::HARLEM RENAISSANCE ORCHESTRA:://