These are the places I’d go if I were visiting my city, in order of preference. I sent this exact list to one of my colleagues visiting from Hong Kong.
Public - My favorite restaurant in the city won a Michelin Star this year. Great ambiance, interesting dishes, great mixed drinks.
El Faro - Really great, real Spanish food, in a super-casual atmosphere. They’ve been open since 1927 in the same spot; this was my parent’s favorite dinner date spot. Have the paella a la valenciana, and/or mariscada with green sauce, and some sangria, then some flan or laruca for dessert. This place is super packed on weekends; it’s best to go early on a weekday.
Casellula - A really great, small wine bar in Hell’s Kitchen/Midtown West with an amazing cheese selection and good lite fare.
Casa Mono - More upscale Spanish restaurant with an amazing wine list.
At least one of Eleven Madison/The Modern/Tabla/Gramercy Tavern - Danny Meyer’s restaurants; Eleven Madison is particularly great (but more expensive than the others), but all are worth visiting. The Modern is inside the MoMA, but eat in the Bar Room; the Dining Room is not worth it. All of them consistently get great reviews and awards, and are known for their great service.
La Esquina - Good Mexican street food upstairs (very informal), dressed up Mexican downstairs (reservations required; good people watching).
Tarallucci e Vino - a nice wine bar-turned-restaurant with a good menu.
I have many, many more, but I’d start with those.