It's not really romantic but Burger Joint inside the Le Parker Meridian is the best burger you will ever eat
Love a good burger joint!
These are great for breakfast/brunch at least, Balthazar is very romantic too...http://grownuptravelguide.com/6-of-the-best-breakfast-joints-in-new...
Serendipity 3 is a must for desserts! But make a reservation about 3-4 weeks in an advance unless you want to wait 1-1,5 hrs for a table (we just went there last Friday and waited for almost 1,5 hrs!)