Where you’re staying makes a big difference, but, any of Philip Guardione’s restaurants are excellent, make reservations online before you go!
https://www.piccolacucinagroup.com/en/
Juliana’s is fantastic for pizza
Eileen’s Special Cheesecake for dessert
Westville has several locations around town for a good meal.
Entertainment is dependent on who you are going with and when, tons of plays and shows are great. Knicks and Nets in winter are basketball options, hockey if you’re in to that. One World Observatory is cool, the other give you a better outdoor experience. Walk the Brooklyn Bridge from Brooklyn to Manhattan (Juliana’s pizza is close to here), visit the High Line for another nice walk with some cool places to shop/eat along the way.