It all depends who is playing where on any given night.

Check out the web site of Time Out New York for info on who is playing where when, and what sort of charge or cover they will have.

Within walking distance is Birdland; see if you can catch Cyrille Amie.

http://www.birdlandjazz.com/

Blue Note is a great venue, and also within a walk of under a half hour:


http://www.bluenote.net/newyork/index.shtml

The cabaret-ish Metropolitan Room is in Flatiron.

http://metropolitanroom.com/index.cfm

Those are low key and not very pricey.

You can also try BB King's; the man himself will play there this week. Even if not jazz, and much more pricey, should be a show worth seeing. They do have some jazz acts, too.

http://www.bbkingblues.com/bio.php?id=1730&utm_source=bluenote&utm_medium=banner&utm_campaign=bbking

Jazz Standard (below Blue Smoke restaurant).

Not in the Flatiron district, but a fantastic venue for jazz is Jazz at Lincoln Center located in the Time Warner bldg in Columbus Circle. They have fabulous jazz and several theaters. They were designed for jazz with wonderful acoustics. The small Allen Room overlooking Central Park is special.

55 Bar is low key great jazz. http://www.yelp.com/biz/the-55-bar-new-york. Bigapplejazz.com has a good listing of places called the jazz bible. Village Vanguard is also low key and great. Agree with CPG that Jazz at Lincoln Center (Dizzy's and the Alen room) is great, but it can get pricey and is more glamorous (great view, nice food) than quirky or funky. The Jazz Standard is sort of quirky.

While the Blue Note is well known and gets good musicians, it's the most uncomfortable, customer unfriendly places in NYC. You wait in line outside, regardless of a reservation; get seated based on your place in line. You're seated with strangers on uncomfortable chairs at small crowded tables and pay a minimum and cover charge for bad drinks. Go only if you HAVE to see whoever is performing.