In the Village....Blue Note, Zinc Bar, Fat Cat, Smalls. For Blues - Terra Blues.
On the Upper West Side...Cleopatra's Needle (Broadway and 93rd), SMOKE (Broadway and 105)
Midtown west...Iridium

There are many others!

Google jazz in NYC and you be taken to a site that lists ALL venues and ALL performers schedule...for every day of the month.

Also the WBGO Jazz Calendar...google it or find it at WBGO.org

Hope this helps. have GREAT fun!

ykc