@Djchickpea HIGHLY recommend a food tour. I did a food truck one a few years back and it was ace. So much fun.
RE: Central Park - the zoo is always worth a visit. Keep an eye on their Instagram for more up-to-date activities. If you like dogs and really want to feel like a local, go before 9am at the weekend. It's off-leash hours and all the locals come out with their coffees and dogs for a stroll. If you hate dogs, go after 9am.
Otherwise, for new stuff, take a look at the Little Island, the Highline Extension and Hudson Yards/Manhattan West. Again, check the instagrams for interesting happenings and free things. Hudson Yards also has an observation deck.
Dirt Candy is a very hip vegetarian restaurant. The Butcher's Daughter is "plant based" but also extremely fashionable atm. Miznon isn't veggie, but they're famous for their vegetable dishes like the roasted cauliflower.
For the best EVER view of the NYC skyline, take yourself to Gantry Plaza Park in Long Island City. It's gorgeous.
If you're daughter's into doing things for the 'gram, the Color Factory and the Museum of Ice Cream are fun, if a bit pricy.