Oh hey my buddy was just visiting NY, so I put together a little list of places I like. I am by no means an expert, but I have been a chef for 17 years, and my family lives in New York, so I am there at least once per year. Most of my recs are in the lower half of Manhattan. I do also have recs for Long Island, as that's where my family is, but most ppl don't get out that far when visiting NY.
My top recommendation is a slice of New York cheesecake at Rocco's. The kind with no crust. But you don't need to specify, if you just order new york cheese cake, that's what they'll bring you. And a cup of earl grey to compliment the flavor.
Rocco's is right around the corner from Joe's Pizza, if you wanna double load on dairy and carbs. But seriously good slices. Of course you can find better at corner shops outside Manhattan, but as far as the city goes, they're one of the best for sure.
If you want more of a sit down meal, Suprema Provisions is an amazing underrated italian place. Their pasta dishes and octopus were done RIGHT.
And then if you're up for a bit of a walk from that area, Swift Hiberian Lounge pours the best pint of guiness in the city, maybe in the country. I don't even like Guiness, but man theirs is something else. They've got decent pub food as well, and live traditional music some nights.
If you like a really good drink, check out Attaboy Speakeasy. It's a bar where you just tell the bartenders what sort of flavors you enjoy, and any other preferences you have, and they will just make you amazing drinks. They don't serve any food.
When you show up to Attaboy, it will seem like it's closed. You have to ring the bell, and someone will come out and put your name on the list. It will likely be a 2+ hour wait, so I recommend putting your name on the list, then taking a taxi across the Brooklyn Bridge. Getting out of the taxi, and walking back across the bridge, back into Manhattan. Then either hoof it or grab a cab back to the speakeasy. That should kill most of the wait time, and the walk across the bridge is absolutely magical. Bring a cup of hot tea or coffee on the walk with you if you can.
I'd love to hear your thoughts if you wind up going to any of these places!