Where to start, there are so many great places? The Chelsea Market is a great place to go for just about anything you want, lots of small restaurants that cover many cuisines for every appetite.
https://dancebeat.com/m-db-articles-en/item/1439-fftmanhattan#sigProIdd6817dae17
https://dancebeat.com/m-db-articles-en/item/1439-fftmanhattan#sigProId2a243bc70b
https://dancebeat.com/m-db-articles-en/item/1439-fftmanhattan#sigProIdfe560ad770
Lilia, Robertas Pizza and The Four Horsemen are others. I hope to explore these while I'm in New York at the Manhattan Dance Championships!