One evening in New York

I'm having a 24-hour layover in New York and have never been before. Rather than sprint around trying to do some tourist itinerary, I just want to have a chilled but rich "New York evening" in Manhattan on 01 March.

Can I get recommendations for:

1- A nice experiential walk where I can get a feel for the vibe

2- A recommendation for an "old New York" restaurant. Somewhere well storied with a nice atmosphere, candle lit and vibrant. I tend to google "Historical restaurants", for example, but a recommendation from someone who knows well would be good. Like, I know Balthazar is famed, but we have one in London which I already enjoy.

3- A nice, chilled lounge/ hotel bar for a nightcap. Somewhere to take a martini and and relax for an hour-or-so.

So, yea, not too much. Quality over quantity. insight over sights. I hope this makes sense!

Much appreciated!