Cherry Lane Theater
Bitter End
Historic music club "New York's Oldest Rock Club" opened in 1961 with legendary 60's acts before they were legendary. Some of the acts to play here include Joan Baez, Judy Collins, Jim Croce, David Crosby, Bob Dylan, Arlo Guthrie...you get the idea. Still has several live acts each night for little or no cover charge. Extremely intimate bar atmosphere.
Village Vanguard
Presents a great lineup of jazz performers in a quiet room except for the music that has good acoustics.
Blue Note
Also has a lineup of famous jazz and blues performers. It feels a little more like a bar with people talking during the show and a little less like a venue that's only about the music.
Small's
A great place to hear excellent jazz at low prices.
Greenwich Village has developed as a home for a significant number of off-Broadway theater companies and lots of music venues.