I love the conjunction of “free,” “jazz,” “festivals,” “summer” and “New York City” Â — though not all free fests are jazz, and not all jazz fests are free (in either of two senses of the word).
For instance, the 17th Vision Festival, which I write up in my CityArts-New York column, has some free shows, and can be aesthetically linked to “free jazz,” but the concerts (for the first time at Roulette in Brooklyn) do have admission charges. Then there’s the Blue Note Jazz Festival 2012, June 10 – 30, performances at the Blue Note, Highline Ballroom, B.B. King’s, the Henry Street Settlement and the Apollo Theater all requiring tickets, and most of the music quite structured — but including one bona fide visitation of a 1960s “Free Jazz” era classic, John Coltrane’s suite “Africa/Brass,” brought to life by original pianist McCoy Tyner and the Charles Tolliver Big Band.
I myself will pontificate freely (and for free) on a Vision Fest panel Thurs., June 14, titled, “Free Music: Why Then/Why Now,” in the estimable company of pianist Dave Burrell, baritone saxophonist Hamiet Bluiett, trumpeter Wadada Leo Smith, multi-instrumentalist/composer Elliott Sharp, all moderated by Scott Currie. The Blue Note Fest does have one no-fee event on its sched: Groove Theory  with Soulive, Riq and Rah (with strings) and dj Q?estlove at Central Park Summerstage, June 17.
Of course Summerstage, a division of the City Parks Foundation program which kicked off its summer season with a benefit Tribute to the Music of Jimi Hendrix blow out on June 5,
is all free –as are the Celebrate Brooklyn! concerts at the Prospect Park Bandshell, which began June 5 with a visit from reggae popularizer Jimmy Cliff, and also the River to River Festival events (at least most of them), June 17 through July 15, around Manhattan’s lower tip and on Governor’s Island.
None of those series are predominantly jazz, though all of them have their jazz, pre-jazz, post-jazz or just jazzy highlights. I’ll name three: pianist Geri Allen with visual artist Carrie Mae Weems’ “Slow Fade To Black” (with Esperanza Spalding, Terri Lyne Carrington, Lizz Wright and Patrice Rushen, among others, 8 pm, Friday June 15, (Celebrate Brooklyn!);  Eddie Palmieri with his AfroCaribbean Jazz Octet at Rockefeller Park (River to River), 7 pm, June 21;  Orchestre Poly-Rhytmo (jazzy, in the Afro-pop manner) from Benin at Summerstage, 3 pm, June 22 .
There are more — check the schedules. All music is in some sense “free.”