It's really the worst and not worth spending a lot of time. I really like to walk if at all possible (vs subway) and just people watch. Central Park is great. The Natural History museum has tons of cool dinosaur stuff if your kids are into it, or the Met is also really great. I might start in Times Sq, walk around on the upper west side and find a place to eat, go to Central Park and hit a museum. That would just about be a day. You could take the subway down to the 9/11 memorial, but it will be a busy day.

It feels futile to make food recommendations. There is no shortage of excellent food so I wouldn't plan a day trip around any one place. My under the radar pizza pick is the montonara starita pizza at Don Antonio. It's lightly fried before finished in a wood oven. Not something you would find easily outside NYC.

I see you're also heading up to New England. I have no shortage of New England recommendations if you're looking for that. Feel free to DM.