Here's a suggestion that I didn't think of... Although it's not
technically BBQ.

How about Kalbi, Bulgoki and Sam-Gyup-Sal (Three Fat Layer Pork... less
known but awesome!) at a Korean place

Although the best korean is in Queens or Fort Lee, NJ. Kang Suh across
Macy's on Broadway isn't too bad. And it was the only place in
Manhattan that I could recall bringing hot lump right to your table.
You just can't go wrong grilling at your own table over Lump!