IMO: there are so many things to see and do in NYC that it dwarfs whatever other attractions there are in the tristate area.
I’m assuming you know about the museums and Lincoln Center and the ferry and all that so I’ll recommend the spots I personally enjoyed.
I would take a day to just stroll through Harlem, it’s a really charming neighborhood full of history. There’s
this place I used to go to for jazz shows on Sundays, superb musicians and amazing home atmosphere.
I loved just walking through Manhattan, by night or day. Above all lower Manhattan, places like Soho and Tribeca and Chelsea. Midtown is much more touristy and the closer you get to Times Square the more crowded the sidewalks get. But still lots and lots of things to see there, I love Bryant Park for one. I once met one your finest, Clarence Seedorf, in Times Square!
NYC isn’t famous for Mexican food to put it mildly but one place you must patronize is
Toloache. Their grasshopper taco, a Oaxacan staple, makes the “you will eat the bugs” meme sound very tempting. A top five protein.
One of the city’s loveliest streets is Arthur Avenue (little Italy) in the Bronx BUT each time I ate there it was middling cafeteria level food. If there’s a good restaurant there I’m not aware of it. I’d go there cause it’s really charming, esp during the fall, but just get an espresso or something. Bronx has an great zoo btw.
Brooklyn: Williamsburg, obviously, is a big one but also all the neighborhoods around Prospect Park are gorgeous and full of great places to eat. Two of my faves are
Werkstatt in Prospect Park South and the Ample Hills creamery in Prospect Heights, though I maintain that Haagen Dazs does a better salted caramel.
My favorite neighborhood of all though must be Astoria, Queens. Lots of great memories.
This is a decent guide
If for some reason you decide to visit the museum of the moving image, you could then grab something to eat at the
Villa Brazil Cafe Grill buffet (great food but only makes sense if you eat meat). If you do, could you hop by the Delicatessen bodega on the corner? It has to be the most unpleasant bodega in the city, run by a very aggressive Chinese lady. Everything is covered in a thick coat of dust. I was lowkey fascinated with it. Curious if it’s still the same, that's all.