Grand Havana Room is membership only, $3000 invitation-only membership then $200/mo.
Club Macanudo - collared shirts only. $30 table minimum, $15 cigar minimum. Appear to have a modest cigar selection.
St. Clouds Rooftop Cigar Lounge at the Knickerbocker Hotel - hadn't heard of this. Assuming it's formal attire only, like Club Macanudo, since it appears to be run by them? Same table/cigar minimum, or more? Looks pricey.
SoHo Cigar Bar - $10 cutting fee or buy a cigar there but beware that the cigar upcharges are outrageous. They charge $100 for Opus X Lost City and I think $50 minimum on ANY Davidoff.
Papa Juan Cigar Room (3456 Broadway) - make their own cigars, don't sell commercial sticks beyond that, right?
(Adding Martinez Hand-Rolled Cigars as they're similar to the above ^ but more central to midtown)
Carnegie Club - also business casual.
I personally go to Cigar Inn (1016 Second Ave) aka Casa de Montecristo several times a week. They have a $10 cutting fee but huge selection of sticks with modest upcharge from what you can get online, friendly/helpful staff and you can find lots of sticks around $10 or even under. Buy a stick and you can smoke your own. Buy two and you can even BYOB. Buy 6 and you get 15% off, buy 25 you get 25% off. Internet, comfy leather chairs, big TVs, open late, etc. They also have Casa Cuba right now for like $8/stick. Super tasty,... very reminiscent of Opus X.
Any of the three Davidoff stores in town are great if you wanna smoke a nicer stick. Way smaller and less lively than Casa de Montecristo. Close earlier, 8PM vs midnight/later. Wider selection of ultra premium sticks like Opus X Lost City and Padron The Hammer (maduro), rarer Davidoffs like Chefs and Year of the... and Royal Release.
Bar & Books is said to be outwardly racist, so be warned. Although they do have a $5 cutting fee. Cigars appear to be way overpriced though.
Nat Sherman Townhouse (12 East 42nd Street). Great spot, my friend works there. It's not a cigar lounge, though, just a store where you can smoke inside if you strictly BUY something (no cutting fee, have to buy). Membership lounge in basement that's like $3k to join. Great selection of sticks though. Rare Nat Sherman blends. Opus X Lost City. Etc. More upcharge than Cigar Inn, but not nearly as much as Bar & Books or Soho.
In NYC...
St. Clouds Rooftop Cigar Lounge at the Knickerbocker Hotel is a really nice spot (6 Times Square, 17th floor).
SoHo Cigar Bar (32 Watts Street).
Cigar Inn (1016 Second Ave).
Carnegie Club (156 West 56th; pricey and sometimes they have exclusive nights so check ahead).
Club Macanudo as someone stated (26 East 63rd Street).
Nat Sherman Townhouse (12 East 42nd Street).
Davidoff of Geneva, Brookfield (225 Liberty Street).
Davidoff of Geneva, 6th Ave (1390 Avenue of the Americas).
Papa Juan Cigar Room (3456 Broadway).
Bar & Brooks (1020 Lexington Ave).
Gran Havana Room (666 5th Ave).
Not really familiar with the Princeton area but there are a few decent lounges, restaurants and bars on your way into the city if you're looking to stop.
Crave Cigars (130 Baldwin Ave, Jersey City).
Tony Santana Boulevard Cigar Shop (1019 Broadway Street, Bayonne).
Cigar Room (206 Main Street, Fort Lee; right over the GW bridge on your way into the city).
Porter House which is now Hearth & Tap (125 North Kinderkamack Road, Montvale; this is my go to spot aside from JR/Casa de Montecristo in Paramus).