The Mingus Big Band plays at the Iridium Jazz club (1650 Broadway) every Tuesday night: http://www.iridiumjazzclub.com/bio.php?id=187
I've been listening to Mingus all day long today. And now that I've had a few beers, I wish I was there, listening to the big band play live. The first time I heard mingus was from the big band when they played downtown 10 years ago. I've seen them maybe 5 times since then, including once at the Beacon Theatre when they played with Elvis Costello. Every single time has been absolutely astounding.
There's an 8pm show and a 10pm show. Cover is hefty: $25, but BELIEVE ME WHEN I TELL YOU IT'S WORTH IT. Is not all-caps convincing enough? I struggle to imagine what else could be. It's not something to do all the time, but it's very, very worth it to do at least once, if not once in a while. There are a few people on here who I've talked to about mingus, and I don't know if you've ever seen the mingus big band...but you should. I'm going next Tuesday.