Central Park
The Met
Madison Avenue
Natural History Museum
Grimaldi's for pizza in downtown Brooklyn
L&B Spumoni Gardens for Sicilian pizza if you;re willing to go deeper into Brooklyn
Katz Deli
Carnagie's Deli (in Times Square...more touristy but still delicious!)
Blue Note Jazz Club or Village Vanguard if you guys like jazz
The Strand Bookstore if you love books
Chelsea market
I would take a tour with a professional guide to get more of a feel of the city and see what they like to do