You probably heard already about the Blue note and the BB king... So...
The really classic "jam to the night" places that I recommend are:
The Fat Cat
Smalls (was close for couple of years and reopened)
both, couple of blocks away from each other, on West 4th st. between Bleecker and MCcdeugel.
you sit there in those small places drink wine and see infont of you musicians like William ash , criss chick etc... absolutely amazing...
Have fun.