Sorry elefantfresh - can't actually find the info. on that jazz place - but I suppose it's the music more so than the venue - I'd definitely advise getting Time Out as soon as you arrive and if the Charles Mingus (big?) band are playing anywhere I'd recommend seeing them - mostly fairly conventional but some mad 'freak-out' modern stuff too.
In general, Greenwich Village and the bordering East Village, West Village and Soho areas will provide a lot to see/do with Washington Sq being a kind of epicentre.
Museums (of Contemporary Art, Guggenheim, African Art & Alternative Museum) are all in the locality. Famous music venues (Blue Note, The Bitter End, CBGBs) are all nearby together with great cafés, bookshops & all sorts of odd places/people.
You'll love it!