Regarding live jazz in NYC, the greatest revelation is that one could start early, end late, and not spend a lot of money: checking out 5 or 6 different clubs all over the city. There are great, relatively expensive world famous clubs like the Village Vanguard, Birdland Jazz Club, Blue Note, Dizzy's, Iridium, Jazz Standard, and Smoke, which regularly present legendary performers.
In the West Village (Greenwich Village around Sheridan Square at 7th Ave. South) there is an explosion of jazz clubs all within a few blocks of each other with free sets of top shelf live jazz (and some blues/R&B/gospel/showtune sing-a-longs/ even chamber music) available. Some of the clubs listed just ask for a 2 drink minimum; one just asks for $3 and is all ages;and a couple have free early sets and charge a $10 - $20 cover for several hours of live music after their earlier free sets. FYI: All these clubs and more are listed on the web, and this is a collection of some in Greenwich Village and Harlem.
Monday Night Jam presented by Jazz Foundation of America: This show has been around for decades. Jazz Foundation hosts a free open jam every Monday 7:00 PM - 9:30 PM. Everyone from big names to up-and-comers come by to hang out and rehearse together.
Smalls: Free sets as early as 4PM, $10-$20 after 7:30PM. Students welcome. Standard bearer for the neighborhood jazz scene. After-hours jam session nightly.
Arthurs Tavern: Always free, oldest club in NYC, with a variety of jazz/blues/house rockers/R&B and the longest running trad jazz band in the city (going on 50 years).
For standing around a piano singing showtunes in an ancient Village basement there's Marie's Crisis Cafe, next door to Arthur's Tavern; and more visibly, on the corner of Christopher and 7th is the Duplex piano bar and cabaret. And for showtune-less piano, try Mezzrow on 7th and 10th.
(Oh yeah, and you don't want to miss out on free, old-school jazz every Sunday 8PM-11PM at the Ear Inn on Spring street. Get there early enough to score a table by trumpeter/bandleader Jon-Erik Kellso and guitarist Matt Munisteri plus an unbelievable roster of special guests musicians rotating through every week). The food is wonderful, and the Ear Inn building is closing in on 200 years of NY history).
A short walk to the east past 6th Ave. will take you to another inexpensive music mecca orbiting around the Blue Note. The jazziest among these are The Bar Next Door on MacDougal, and Zinc Bar on West 3rd - each with excellent jazz credentials and a decidedly more dimly lit, romantic vibe then the places mentioned above, and both featuring vocalists on Monday nights. These clubs have cover charges of $10 -$15 and the Bar Next Door serves limited menu Italian fare.
Hidden jazz haunts in the Village heading East that must not go unmentioned are Knickerbocker for knock out duos and trios and steak; The Stone in the East Village for stripped-down, bare-knuckled avant-garde; Jules Bistro for the French perspective; and finally 5C, Nublu, Nuyorican, Also, an underground late night Tuesday trad jazz jam has erupted at Mona's on Ave. B.
Jumping up to Harlem, there is a nice concentration of live jazz venues in the Central Harlem district that made jazz a household word in the post WWI period dubbed The Jazz Age by F. Scott Fitzgerald. The area around the original Swing Street, West 133rd and 7th Ave. (now Adam Clayton Powell, Jr. Blvd), is home to 6 important joints on the uptown jazz map. All 6 are remarkable in their own way, and all 6 are affordable and supported by the neighborhood as well as visitors from around the world (even without the support of a website in 3 cases). Word of mouth trumps all.
Paris Blues: No cover and Free chicken, rice and beans. Two drink minimum. Live Jazz Bands 7 nights ( 9 PM - 1 AM) a week and three bands on Sunday, alternating Latin Jazz Bands (5-9) and then Melvin Vines and the Harlem Jazz Machine (9 -1). All Bands perform 3 sets and allow instrumentalist and vocalist alike to sit in! This Harlem's oldest and only remaining live Jazz dive and you are like to see Sam Hargress, Owner, Cook and still Manager glad handing the crowd as well as tv, film, and stage and of course Jazz legends in the crowd.
Bill’s Place: $20 cover for 2 sets of no-holds-barred, take-no-prisoners, blood and guts jazz only on Fridays and Saturdays. Pile in by 9PM for the first set (11PM for the 2nd set), and enjoy the one-of-a-kind fantasy of hearing Bill Saxton and the Young Musicians of New York that he discovers, deliver the goods in a 1920's prohibition era speakeasy right on 133rd Street. 148 W.133rd Street, said to be the place where Billie Holiday was discovered by John Hammond in the early 30's.