Lots of choice, lots of chains & lots of really good places. Budget (& whether you are travelling with children/their ages) will massively influence your choices. I recommend looking at YouTube for 'Best xxx' videos and seeing what takes your fancy. Here are places we visited Feb 17:
Shake Shack for fast food joint... But expect long queues and no seating in peak times
Momofuki - noodles & Asian cuisine
Tavern on the Green - food good & £££ but it's in all the movies!
Burger Joint (hidden in Le Parker Meridian) - amazing burger & quiet a cool vibe. Like a fast food joint but inside a posh hotel!
Levain Bakery for cookies, cakes & coffee
Ellas Starlight Diner - cutesy, tourist trsp 50's style diner with singing & dancing... but your a tourist & it's on Broadway!
Waffles & Dinges - not a restaurant but a food cart with the most amazing waffles, pancake and ice cream desserts
Mothers Ruin - not been personally but lots of recommendations