I've been to a few
SoHo Cigar Bar - Very laid back, looks more like a regular bar. Nice vibe, old school pictures of the rat pack on the walls. You could wear anything.
Hudson bar and books - a little more upscale. Not much seating inside. Good to go if you want to sit outside, but there isn't a lot of seating outside. Maybe you could reserve an outdoor seat but I don't know. I think you could wear anything.
Lexington bar and books - same owners as Hudson, but a little more upscale and I don't think there's outdoor seating. I believe there's a dress code.
I heard Carnegie club is nice, I think Saturday night they have a band that plays Sinatra. There's also macanudo club
I like a libation with my smoke so it's worth it to know that some of the places mentioned above won't serve alcohol. I guess the cigar shops like davidoff, barclay rex, Casa montecristo
Not sure if you're bringing your own cigars. I believe soho, Hudson, and Lexington wave the cutting fee if you buy a couple of drinks. Not sure about Carnegie and macanudo but they may not.