I just got back from New York and have some great suggestions for you. Sorry, they're all on the pricey side, but worth it.
Italian: Anthony's on Mulberry Street, La Giarra 3rd Ave/34th Street
Japanese: Morimoto 88 Tenth Ave, 212-989-8883. Check out the bathrooms, you'll be in for a surprise.
Eleven Madison Park - 11 Madison Ave. 212-889-0905
French: Fleur de Sel 5 East 20th st. 212-460-9100
Enjoy!