Out of my experience:

  1. Ophelia at the Beekman Tower

First off, I have great affection for the name ‘Ophelia’. And there’s a cute history behind this place: this art-deco style rooftop bar” originally served as a womens-only club and hotel space for the national Greek-letter sororities” — I wish they still have ladies only places nowadays. Located on the 26th floor of the Beekman tower, you will get a wonderful night view of lower manhattan including the Empire State building.
I went with my friend on a Saturday night for my birthday. It was REALLY packed and busy. Although I had made a reservation we still have to wait for quite some time to get seated. But well it’s Saturday and it’s Manhattan, and they really just a few tables in total what else can you expect. Tbh the drink was pretty nice and the view was awesome, and items were fairly priced, it was a nice visit. My first drink was ‘purple tuxedo’ with EMPRESS 1908 GIN as base, something that was hyped for a while if I remember it right. It was a symphony of herbal and fruity notes, and I love the dash of absinthe. My friend ordered ‘Far east side’, just reminds me of many similar citrus cocktails (sidecar, screwdriver, etc), too light for my taste but I still think it’s well-done. The final one we ordered ‘Ophelia’s ascension’, probably one of the popular drinks on the menu, and surely we were not disappointed. The smoky yet smooth taste is so unique, and the drink was pouring out from a ‘magic pot’ into the glass made me feel like I was drinking some kind of magik potion x.

On my list:

THE RAINES LAW ROOM

48 W 17th Street
New York NY 10011
A speakeasy with beautiful historical interior design (one article said Victorian… well maybe Victorian-inspired or ummm, flavored). Pretty neat to use the raine law as inspiration and the menu looks cool, too.

Apotheke Mixthology

Man a speakeasy cocktail bar in Chinatown located at the ‘bloody angle’ where gangsters used to frequently open fire back in the 1900s, and they have a remarkable collection of absinthe. So yeah, def will visit someday.

The Campbell Apartment

Grand Central Terminal at 15 Vanderbilt Avenue

Also a really cool place that used to look like this:

All the history that's going to die with the Campbell Apartment

the architecture is amazing.

More source:

Top 3 speakeasy bars in New York – by My Hotel Life

Bonus:

The Trinity Place

115 Broadway   
New York

It’s not a bar, but a restaurant situated inside a wall street bank vault. Not sure the most relaxing and comfortable place to dine but what an experience.